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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields GROS, M., Regulateurs syntomiques et valeurs de functions L ^-adiques I (wit Appendix by Kurihara, M. ), Inventiones math. 99 (1990) 293-320. Zentralblatt MATH: Arithmetic varieties and schemes; Arakelov theory; heights, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, \(p\)-adic cohomology, crystalline cohomology, Local ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Cubic and quartic Diophantine equations, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Shaska, T.; Beshaj, L., Heights on algebraic curves.Advances on superelliptic curves and their applications, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur. 41, 137-175, (2015), IOS, Amsterdam Heights, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Algebraic theory of abelian varieties, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Stoll, M.: On the arithmetic of the curves y2=x\(\ell +A\), II. J. number theory 93, 183-206 (2002) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields \beginbarticle ----, \batitleArithmetic fake projective spaces and arithmetic fake Grassmannians, \bjtitleAmer. J. Math. \bvolume131 (\byear2009), no. \bissue2, page 379-\blpage407. \endbarticle \OrigBibText Gopal Prasad and Sai-Kee Yeung. Arithmetic fake projective spaces and arithmetic fake Grassmannians. Amer. J. Math. , 131(2):379-407, 2009. \endOrigBibText \bptokstructpyb \endbibitem Modular and Shimura varieties, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Y. Takeda, A relation between standard conjectures and their arithmetic analogues , Kodai Math. J. 21 (1998), 249--258. Arithmetic varieties and schemes; Arakelov theory; heights, Parametrization (Chow and Hilbert schemes)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Nakashima, T., Construction of codes from Arakelov geometry, Des. codes cryptogr., 73, 47-54, (2014) Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic varieties and schemes; Arakelov theory; heights, Vector bundles on curves and their moduli
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic aspects of modular and Shimura varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Bismut, J.-M. : Torsion analytique équivariante d'une suite exacte courte de fibrés holomorphes , C.R. Acad. Sci. Paris 316, série I (1993) 579- 584. Holomorphic bundles and generalizations, Arithmetic varieties and schemes; Arakelov theory; heights, Connections (general theory), Complex supergeometry, Riemann-Roch theorems
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields S. Bloch, H. Gillet, and C. Soulé, Non-Archimedean Arakelov theory, J. Algebraic Geom. 4 (1995), no. 3, 427 -- 485. Arithmetic varieties and schemes; Arakelov theory; heights, Local ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Riemann-Roch theorems, Arithmetic varieties and schemes; Arakelov theory; heights, Group actions on varieties or schemes (quotients), Index theory and related fixed-point theorems on manifolds, Determinants and determinant bundles, analytic torsion
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Collections of abstracts of lectures, Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to number theory, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Boxall, J., Grant D.: Examples of torsion points on genus two curves. Trans. Am. Math. Soc. 352, 4533--4555 (2000) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Shalika J., Takloo-Bighash R., Tschinkel Y.: Rational points on compactifications of semisimple groups. J. Amer. Math. Soc. 20, 1135--1186 (2007) Rational points, Heights, Representation-theoretic methods; automorphic representations over local and global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields H. Chen, Differentiability of the arithmetic volume function, J. Lond. Math. Soc. (2) 84 (2011), no. 2, 365-384. Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Higher degree equations; Fermat's equation, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Levin, Aaron, Variations on a theme of Runge: effective determination of integral points on certain varieties, J. Théor. Nombres Bordeaux, 20, 2, 385-417, (2008) Varieties over global fields, Heights, Diophantine equations in many variables, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Modular and Shimura varieties, Arithmetic varieties and schemes; Arakelov theory; heights, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Arithmetic aspects of modular and Shimura varieties, Theta series; Weil representation; theta correspondences
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields ZarhinTAMS \bysame , \emph Two-dimensional families of hyperelliptic jacobians with big monodromy, Trans. Amer. Math. Soc. \textbf 368 (2016), no.~5, 3651--3672. Jacobians, Prym varieties, Algebraic theory of abelian varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields G. Freixas i Montplet. An arithmetic Hilbert-Samuel theorem for pointed stable curves. \textit{J. Eur. Math. Soc. (JEMS)}, (2)\textbf{14} (2012), 321351 Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields U. Derenthal and D. Loughran, Singular del Pezzo surfaces that are equivariant compactifications, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 377 (2010), no. Issledovaniya po Teorii Chisel. 10, 26 -- 43, 241 (English, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 171 (2010), no. 6, 714 -- 724. Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Fano varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Teichmüller theory for Riemann surfaces
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields V. V. Batyrev and Y. Tschinkel, ''Rational points of bounded height on compactifications of anisotropic tori,'' Internat. Math. Res. Notices, iss. 12, pp. 591-635, 1995. Rational points, Toric varieties, Newton polyhedra, Okounkov bodies, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Soulé, C., Successive minima on arithmetic varieties , Compos. Math. 96 (1995), 85-98. Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Heights, Elliptic and modular units, Algebraic functions and function fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Counting solutions of Diophantine equations, Rational points, Other Dirichlet series and zeta functions, Modular and Shimura varieties, Heights, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Nekovář, J.: Beilinson's conjectures. In: Motives (Seattle, WA, 1991), Proc. Symp. Pure Math., \textbf{55} Part I, 537-570, Am. Math. Soc., Providence, RI (1994) Arithmetic varieties and schemes; Arakelov theory; heights, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Integration on analytic sets and spaces, currents
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Abelian varieties of dimension \(> 1\), Transcendence (general theory), Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Modular and Shimura varieties, Arithmetic ground fields for curves, Coverings of curves, fundamental group, Special divisors on curves (gonality, Brill-Noether theory)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields \textsc{M. Baker and R. Rumely}, Potential Theory and Dynamics on the Berkovich Projective Line, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2010. Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory, Local ground fields in algebraic geometry, Rigid analytic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Dynamical systems on Berkovich spaces, Non-Archimedean Fatou and Julia sets, Potentials and capacities on other spaces, Other generalizations (nonlinear potential theory, etc.)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Arithmetic aspects of modular and Shimura varieties, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Rational points, Modular and Shimura varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic aspects of modular and Shimura varieties, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields D. Roessler,An Adams-Riemann-Roch theorem in Arakelov geometry, Duke Mathematical Journal96 (1999), 61--126. Riemann-Roch theorems, Arithmetic varieties and schemes; Arakelov theory; heights, \(K\)-theory of schemes, Applications of methods of algebraic \(K\)-theory in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Gil, José Ignacio Burgos; Moriwaki, Atsushi; Philippon, Patrice; Sombra, Martín: Arithmetic positivity on toric varieties, (October 2012) Toric varieties, Newton polyhedra, Okounkov bodies, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Jacobians, Prym varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Complex multiplication and moduli of abelian varieties, Applications to coding theory and cryptography of arithmetic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Burgos, J. I.; Freixas, G.; Litcanu, R., The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms, Ann. Fac. Sci. Toulouse Math. (6), 23, 3, 513-559, (2014) Arithmetic varieties and schemes; Arakelov theory; heights, Riemann-Roch theorems
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Discontinuous groups and automorphic forms, Singularities of curves, local rings, Étale and other Grothendieck topologies and (co)homologies
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Coverings of curves, fundamental group
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Edixhoven, Bas, Arithmetic part of Faltings's proof.Diophantine approximation and abelian varieties, Soesterberg, 1992, Lecture Notes in Math. 1566, 97-110, (1993), Springer, Berlin Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, \(p\)-adic cohomology, crystalline cohomology, Motivic cohomology; motivic homotopy theory
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Complex multiplication and abelian varieties, Complex multiplication and moduli of abelian varieties, Quaternion and other division algebras: arithmetic, zeta functions, Heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields M. H. Baker: Lower bounds for the canonical height on elliptic curves over abelian extensions. Int. Math. Res. Not. 2003 (2003), 1571--1589. Heights, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields GASBARRI (C.) . - Accouplement de Deligne et hauteurs de Néron-Tate , C. R. Acad. sci. Paris, t. 323, série I, 1996 . MR 97j:14026 | Zbl 00952496 Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Modular and Shimura varieties, Formal groups, \(p\)-divisible groups, Arithmetic varieties and schemes; Arakelov theory; heights, Local ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Kudla, S. S.; Rapoport, M., Cycles on Siegel threefolds and derivatives of Eisenstein series, Ann. Sci. Éc. Norm. Supér. (4), 33, 695-756, (2000) Arithmetic aspects of modular and Shimura varieties, Heights, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Fourier coefficients of automorphic forms, Modular and Shimura varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Heights, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Hindry, M.; Pacheco, A., An analogue of the Brauer-Siegel theorem for abelian varieties in positive characteristic, Mosc. Math. J., 16, 1, 45-93, (2016) Elliptic curves over global fields, Arithmetic ground fields for abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Global ground fields in algebraic geometry, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic ground fields for curves, Complex multiplication and moduli of abelian varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Theta functions and abelian varieties, Computational aspects of algebraic curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Viada, Evelina, Nondense subsets of varieties in a power of an elliptic curve, Int. Math. Res. Not. IMRN, 1073-7928, 7, 1213-1246, (2009) Subvarieties of abelian varieties, Elliptic curves over global fields, Heights, Arithmetic ground fields for curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields McKinnon D.: Vojta's main conjecture for blowup surfaces. Proc. Am. Math. Soc. 131(1), 1--12 (2003) (electronic) Elliptic curves over global fields, Varieties over global fields, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields F. Catanese; R. Pignatelli, Pignatelli R., Fibrations of low genus. I, Ann. Sci. école Norm. Sup. (4), 39, 1011-1049, (2006) Surfaces of general type, Fibrations, degenerations in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Benjamin Collas, ''Action of a Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups of genus one'', Int. J. Number Theory 8 (2012) no. 3, p. 763-787 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Achter, Jeffrey D.; Howe, Everett W., Split abelian surfaces over finite fields and reductions of genus-2 curves, Algebra Number Theory, 11, 1, 39-76, (2017) Arithmetic ground fields for abelian varieties, Abelian varieties of dimension \(> 1\), Curves over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Andreas-Stephan Elsenhans and Jörg Jahnel, On the arithmetic of the discriminant for cubic surfaces, J. Ramanujan Math. Soc. 27 (2012), no. 3, 355 -- 373. Varieties over global fields, Arithmetic ground fields for surfaces or higher-dimensional varieties, Fano varieties, Heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields S.-I. Ih, Height uniformity for algebraic points on curves, Compos. Math. 134 (2002), no. 1, 35-57. Varieties over global fields, Heights, Rational points, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Abelian varieties of dimension \(> 1\), Research exposition (monographs, survey articles) pertaining to number theory, Transcendence (general theory), Arithmetic varieties and schemes; Arakelov theory; heights, Research exposition (monographs, survey articles) pertaining to algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Brumer, Armand; McGuinness, Oisín., The behavior of the Mordell-Weil group of elliptic curves, Bull. Amer. Math. Soc. (N.S.), 23, 2, 375-382, (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Computational aspects of algebraic curves, Elliptic curves, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Bost, J.-B.; Mestre, J.-F.; Moret-Bailly, L., \textit{sur le calcul explicite des 'classes de chern' des surfaces arithmétiques de genre 2 [on the explicit calculation of the 'chern classes' of arithmetic surfaces of genus 2]}, Séminaire sur les pinceaux de courbes elliptiques (Paris, 1988), 69-105, (1990), Société Mathématique de France Arithmetic varieties and schemes; Arakelov theory; heights, Theta functions and abelian varieties, Families, moduli of curves (algebraic), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic moduli of abelian varieties, classification
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Ratazzi N., Intersection de courbes et de sous-groupes, et problèmes de minoration de hauteur dans les variétés abéliennes C.M. À paraître aux Annales de l'Institut Fourier. Heights, Abelian varieties of dimension \(> 1\), Results involving abelian varieties, Complex multiplication and abelian varieties, Other abelian and metabelian extensions
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields [26] Oh (H.).-- Orbital counting via mixing and unipotent flows. In ''Homogeneous flows, moduli spaces and arithmetic'', M. Einsiedler et al eds., Clay Math. Proc. 10, Amer. Math. Soc., p.~339-375 (2010). &MR~26 Heights, Varieties over global fields, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems, Rational points, Representations of Lie and linear algebraic groups over global fields and adèle rings, Homogeneous flows, Ergodicity, mixing, rates of mixing
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields C. Consani and M. Marcolli, Archimedean cohomology revisited. In Noncommutative geometry and number theory , Aspects Math. E37, Vieweg, Wiesbaden 2006, 109-140. Arithmetic varieties and schemes; Arakelov theory; heights, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Varieties over global fields, Noncommutative global analysis, noncommutative residues, Noncommutative algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Poonen, B, Gonality of modular curves in characteristic \(p\), Math. Res. Lett., 15, 265-271, (2008) Hypersurfaces and algebraic geometry, Finite ground fields in algebraic geometry, Zeta and \(L\)-functions in characteristic \(p\), Other Dirichlet series and zeta functions, Arithmetic varieties and schemes; Arakelov theory; heights, Projective techniques in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Flynn, E.V., Testa, D.: Finite weil restrictions of curves. arXiv:1210.4407v3, 19 May 2013 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields K. Köhler and D. Roessler,Un théorème du point fixe de Lefschetz en géométrie d'Arakelov, Comptes Rendus de l'Académie des Sciences, Paris, Série I326 (1998), 719--722. Arithmetic varieties and schemes; Arakelov theory; heights, Riemann-Roch theorems, Applications of methods of algebraic \(K\)-theory in algebraic geometry, \(K\)-theory of schemes
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Burgos Gil, José Ignacio; Feliu, Elisenda; Takeda, Yuichiro, On Goncharov's regulator and higher arithmetic Chow groups, Int. Math. Res. Not. IMRN, 1073-7928, 1, 40-73, (2011) Arithmetic varieties and schemes; Arakelov theory; heights, (Equivariant) Chow groups and rings; motives
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Class numbers, class groups, discriminants, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Halle, L. H.: Galois actions on Néron models of Jacobians, Ann. inst. Fourier 60, No. 3, 853-903 (2010) Fibrations, degenerations in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Positive characteristic ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties, Picard schemes, higher Jacobians
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to differential geometry, Proceedings, conferences, collections, etc. pertaining to global analysis, Zeta and \(L\)-functions: analytic theory, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic varieties and schemes; Arakelov theory; heights, Cycles and subschemes, Proceedings of conferences of miscellaneous specific interest
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Karl Rubin, Abelian varieties, \?-adic heights and derivatives, Algebra and number theory (Essen, 1992) de Gruyter, Berlin, 1994, pp. 247 -- 266. \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Local ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Complete intersections
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Quadratic forms over global rings and fields, Varieties over global fields, Estimates on character sums, Primes represented by polynomials; other multiplicative structures of polynomial values, Asymptotic results on arithmetic functions, Goldbach-type theorems; other additive questions involving primes, Arithmetic theory of algebraic function fields, Étale and other Grothendieck topologies and (co)homologies, Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Y. Ônishi, ''Determinant Expressions for Hyperelliptic Functions (with an appendix by S. Matsutani),'' Proc. Edinb. Math. Soc. 48(3), 705--742 (2005); math.NT/0105189. Theta functions and curves; Schottky problem, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic algebraic geometry (Diophantine geometry), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Chen, H.: Maximal slope of tensor product of Hermitian vector bundles. J. Algebraic Geom. \textbf{18}(3), 575-603 (2009) Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Hain, Rational points of universal curves, J. Amer. Math. Soc. 24 pp 709-- (2011) Rational points, Other nonalgebraically closed ground fields in algebraic geometry, Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields EPFL IC LACAL.: PlayStation 3 computing breaks \(2^{60}\) barrier 112-bit prime ECDLP solved. Available at http://lacal.epfl.ch/112bit_prime (2009) Applications to coding theory and cryptography of arithmetic geometry, Heights, Elliptic curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields N. Bruin, E.V. Flynn,Towers of 2-covers of hyperelliptic curves, Trans. Amer. Math. Soc. 357 (2005), 4329-4347. Zbl1145.11317 MR2156713 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields G. Frey and E. Kani, Projective p-adic representations of the k-rational geometric fundamental group, Archiv der Mathematik 77 (2001), 32--46. Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Higher degree equations; Fermat's equation, Plane and space curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Poonen, B, The classification of rational preperiodic points of quadratic polynomials over \({ Q}\): a refined conjecture, Math. Z., 228, 11-29, (1998) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Hilbertian fields; Hilbert's irreducibility theorem, Polynomials (irreducibility, etc.), Heights, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Galbraith, SD, Rational points on \(X_0^+(p)\), Exp. Math., 8, 311-318, (1999) Rational points, Elliptic curves over global fields, Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Corentin Pontreau, A Mordell-Lang plus Bogomolov type result for curves in \?²_{\?}, Monatsh. Math. 157 (2009), no. 3, 267 -- 281. Varieties over global fields, Heights, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Gaël Rémond and Evelina Viada, Problème de Mordell-Lang modulo certaines sous-variétés abéliennes, Int. Math. Res. Not. 35 (2003), 1915 -- 1931 (French). Abelian varieties of dimension \(> 1\), Heights, Results involving abelian varieties, Global ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Zarhin Yu.G. (2006). Non-isogenous superelliptic jacobians. Math. Z. 253: 537--554 Jacobians, Prym varieties, Isogeny, Curves of arbitrary genus or genus \(\ne 1\) over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Quadratic and bilinear Diophantine equations, Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Jacobians, Prym varieties, Computer solution of Diophantine equations, Global ground fields in algebraic geometry, Other nonalgebraically closed ground fields in algebraic geometry, Arithmetic ground fields for curves, Elliptic curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Dominique Bernardi, Hauteur \?-adique sur les courbes elliptiques, Seminar on Number Theory, Paris 1979 -- 80, Progr. Math., vol. 12, Birkhäuser, Boston, Mass., 1981, pp. 1 -- 14 (French). Elliptic curves over global fields, Heights, Local ground fields in algebraic geometry, Theta functions and abelian varieties, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields J.H. Conway and R.A. Parker , On the Hurwitz number of arrays of group elements . Preprint [DFr1] P. Dèbes and M. Fried , Arithmetic variation of fibers , J. für die reine und angew. Math 400 ( 1990 ), 106 - 137 . Zbl 0699.14033 Ramification problems in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Separable extensions, Galois theory, Coverings of curves, fundamental group
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Quadratic and bilinear Diophantine equations, Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Modular and Shimura varieties, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Bost, J.-B., and K. Künnemann, ``Hermitian vector bundles and extension groups on arithmetic schemes, II: The arithmetic Atiyah extension, Astérisque , vol. 327 (2009), pp. 361-424. Arithmetic varieties and schemes; Arakelov theory; heights, Results involving abelian varieties, Sheaves and cohomology of sections of holomorphic vector bundles, general results
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