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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. Diem, A study on theoretical and practical aspects of Weil-restrictions of varieties, Dissertation, 2001. http://www.math.uni-leipzig.de/~diem/dissertation\_diem.dvi Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for abelian varieties, Abelian varieties of dimension \(> 1\), Applications to coding theory and cryptography of arithmetic geometry, 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 Local ground fields in algebraic geometry, Topological properties in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Varieties over finite and local 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 Varieties over global fields, Global ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic varieties and schemes; Arakelov theory; heights, Zeta functions and \(L\)-functions of number fields, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
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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, Arithmetic ground fields for curves, 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 Krattenthaler, C.; Rivoal, T., Multivariate \(p\)-adic formal congruences and integrality of Taylor coefficients of mirror maps.Arithmetic and Galois theories of differential equations, Sémin. Congr. 23, 241-269, (2011), Soc. Math. France, Paris Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Diophantine approximation, transcendental number theory, Calabi-Yau manifolds (algebro-geometric aspects), Other hypergeometric functions and integrals in several variables
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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 [9] S. Zhang: Heights and reductions of semi-stable varieties, Compositio Math. 104 (1996), 77-105. Varieties over global fields, 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 S. S. Kudla, M. Rapoport, and T. Yang, ''On the derivative of an Eisenstein series of weight one,'' Internat. Math. Res. Notices, iss. 7, pp. 347-385, 1999. Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Fourier coefficients of automorphic forms, Forms of half-integer weight; nonholomorphic modular forms, \(L\)-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 Subdirect products and subdirect irreducibility, 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 Hein, G.: Green currents on Kähler manifolds. The ubiquitous heat kernel. Contemp. Math., 398, pp. 245--256. Amer. Math. Soc., Providence (2006) Heat and other parabolic equation methods for PDEs on manifolds, Kähler manifolds, Heat kernels in several complex variables, 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 Jorgenson, J., Kramer, J.: Bounds on Faltings's delta function through covers. Ann. Math. (2) \textbf{170}(1), 1-43 (2009) Arithmetic varieties and schemes; Arakelov theory; heights, Heat and other parabolic equation methods for PDEs on manifolds, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Structure of modular groups and generalizations; arithmetic groups
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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 (Co)homology theory 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, Rational points, 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. A. Corn and T. M. Corn, \textit{Mathematical Handbook for Scientists and Engineers} (McGraw-Hill, New York, 1961). Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry, \(K3\) surfaces and Enriques surfaces, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Varieties 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 Varieties over global fields, Elliptic curves over global fields, Rational points, 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 C. Consani and M. Marcolli, ''Spectral triples from Mumford curves,'' Int. Math. Research Notices 36, 1945--1972 (2003). Curves of arbitrary genus or genus \(\ne 1\) over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Local ground fields in algebraic geometry, Symbolic dynamics, Noncommutative dynamical systems, Noncommutative global analysis, noncommutative residues
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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 Yu. G. Zarhin, ''Local heights and Néron pairings,'' In:Tr. Mat. Inst. Rossiisk. Akad. Nauk, Vol. 208 (1995), pp. 111--127. 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 Yu. I. Manin, et\! \lccYu. Tschinkel, Points of bounded height on del Pezzo surfaces , Compositio Math. 85 (1993), 315--332. Arithmetic ground fields for surfaces or higher-dimensional 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 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Computer solution of Diophantine equations
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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 [13]R. Rumely, A new equivariant in nonarchimedean dynamics, in preparation. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry, 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 F. Amoroso et S. David, Distribution des points de petite hauteur dans les groupes multiplicatifs. Ann. Scuola Norm. Sup. Pisa Série V 3 (2004) 325-348. Zbl1150.11021 MR2075986 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 Lang, S.: Survey of Diophantine geometry. (1997) Arithmetic algebraic geometry (Diophantine geometry), Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic problems in algebraic geometry; Diophantine geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Elliptic curves over global fields, Abelian varieties of dimension \(> 1\), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Diophantine equations, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Global ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for abelian varieties, Measures of irrationality and of transcendence
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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. Zannier, \(Some Problems of Unlikely Intersections in Arithmetic and Geometry (with Appendixes by D. Masser)\). Annals of Mathematics Studies, vol. 181 (Princeton University Press, Princeton, 2012) Research exposition (monographs, survey articles) pertaining to algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Modular and Shimura varieties, 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 Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Linear Diophantine equations, Diophantine inequalities, 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 Elliptic curves, 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 M. Nakamaye , Intersection Theory and Diophantine Approximation. to appear , Journal of Algebraic Geometry. MR 1658224 | Zbl 0953.11026 Diophantine approximation, transcendental number theory, 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 Abelian varieties of dimension \(> 1\), Heights, Complex multiplication and 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 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), 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 Wan, D. Q., On the lang-Trotter conjecture, J. Number Theory., 35, 3, 247-268, (1990) Elliptic curves, Arithmetic varieties and schemes; Arakelov theory; heights, Density theorems, Singularities of curves, local rings
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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 DOI: 10.1016/j.jnt.2005.11.007 Varieties over global fields, Rational points, 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 Adèle rings and groups, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic algebraic geometry (Diophantine 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 Buium, A; Saha, A, The first \(p\)-jet space of an elliptic curve: global functions and lifts of Frobenius, Math. Res. Lett., 21, 677-689, (2014) Local ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; 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 Robinson, R.: An essentially undecidable axiom system. In: Proceedings of the International Congress of Mathematicians 1950, vol. 1, pp. 729-730. American Mathematical Society, Providence (1952) Rational points, Varieties over global fields, Heights, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Plane and space curves, Erdős problems and related topics of discrete 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
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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 \(> 1\), Arithmetic ground fields for abelian varieties, Analytic theory of abelian varieties; abelian integrals and differentials, 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 Families, moduli of curves (algebraic), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, 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 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Heights, Zeta functions and related questions in algebraic geometry (e.g., 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 T. MIYANO AND J. NOGUCHI, Moduli spaces of harmonic and holomorphic mappings and Diophantin geometry, in ''Prospects in Complex Geometry'', Proc. 25th Taniguchi International Symposium, Katata/Kyoto, 1989 J. Noguchi and T. Ohsawa, eds., Lecture Notes in Math. 1468, Springer-Verlag, Heidelberg, 1991, 227-253. Harmonic maps, etc., 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 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry, 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 Varieties over global fields, Rational points, Diophantine approximation, transcendental number theory, Nevanlinna theory; growth estimates; other inequalities of several complex variables
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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 Good, A.: The convolution method for Dirichlet series. In: \textit{The Selberg trace formula and related topics (Brunswick, Maine, 1984)}, volume~53 of \textit{Contemp. Math.}, pages 207-214. Amer. Math. Soc., Providence, RI, (1986) Varieties over global fields, Group actions on varieties or schemes (quotients), Arithmetic varieties and schemes; Arakelov theory; heights, Semisimple Lie groups and their representations, Differential geometry of symmetric spaces
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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 Martine Girard, Groupe des points de Weierstrass sur une famille de quartiques lisses, Preprint, December 1999. Riemann surfaces; Weierstrass points; gap sequences, 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 Theta series; Weil representation; theta correspondences, Lattice packing and covering (number-theoretic aspects), Lattices and convex bodies (number-theoretic aspects), 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 Dynamical systems over global ground fields, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems, Heights, Rational and birational maps
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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 T. Ono: On Shafarevich-Tate sets. Proc. The 7th MSJ Int. Res. Inst. Class Field Theory-its centenary and prospect (to appear). Galois cohomology, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Automorphisms of 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 Noam D. Elkies, Points of low height on elliptic curves and surfaces. I. Elliptic surfaces over \Bbb P\textonesuperior with small \?, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 4076, Springer, Berlin, 2006, pp. 287 -- 301. Heights, Elliptic curves 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 Flynn, EV, Descent via (5,5)-isogeny on Jacobians of genus 2 curves, J. Number Theory, 153, 270-282, (2015) 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 Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings of conferences of miscellaneous specific interest, Arithmetic varieties and schemes; Arakelov theory; heights, Dessins d'enfants theory, Distribution of primes, Minima of forms, Arithmetic aspects of dessins d'enfants, Belyĭ theory, Other special functions, Actions of groups on commutative rings; invariant 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 Bremner, A.: Some interesting curves of genus 2 to 7. J. Number Theory 67, 277-290 (1997) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, 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 Hindes, W., The arithmetic of curves defined by iteration, Acta Arith., 169, 1-27, (2015) Rational points, Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, Separable extensions, Galois theory, Dynamical systems over global ground fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Special algebraic curves and curves of low genus, Groups acting on trees, Arithmetic dynamics on general algebraic varieties, 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 Kim, C.H., Koo, J.K.: Estimation of genus for certain arithmetic groups. Commun. Algebra 32(7), 2479--2495 (2004) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Riemann surfaces; Weierstrass points; gap sequences
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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 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 Siksek S., Explicit Chabauty over number fields, Algebra Number Theory 7 (2013), no. 4, 765-793. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Analytic theory of abelian varieties; abelian integrals and differentials, Divisors, linear systems, invertible sheaves
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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 Brylinski, J.-L.: Heights for local systems on curves, Duke Math. J.59, 1--26 (1989) Arithmetic varieties and schemes; Arakelov theory; heights, Generalizations (algebraic spaces, stacks), Global ground fields in algebraic geometry, 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, Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Relations with algebraic geometry and topology, Other groups and their modular and automorphic forms (several variables), Riemann-Roch theorems, \(K3\) surfaces and Enriques 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 Algebraic cycles, 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, Continued fractions, 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, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, 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 Tzermias, P, Low-degree points on Hurwitz-Klein curves, Trans. Am. Math. Soc., 356, 939-951, (2003) Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, 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 Manin, Y.I.: The Tate height of points on an abelian variety. Its variants and applications, Izv. Akad. Nauk S.S.S.R., Ser. Mat.28, 1363--1390 (1964);A.M.S. Translations, Ser. 2,59, 82--110 (1966) 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 Gasbarri, C., \textit{analytic subvarieties with many rational points}, Math. Ann., 346, 199-243, (2010) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Arithmetic varieties and schemes; Arakelov theory; heights, Germs of analytic sets, local parametrization, Value distribution theory in higher dimensions, Kähler manifolds
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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 Tetsuji Shioda, ``On the Mordell-Weil lattices'', Comment. Math. Univ. St. Pauli39 (1990) no. 2, p. 211-240 Rational points, Elliptic curves, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves over global fields, 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 Rational points, Group actions on varieties or schemes (quotients), 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 Siksek, S, Chabauty for symmetric powers of curves, Algebra Number Theory, 3, 209-236, (2009) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Varieties over global fields, Analytic theory of abelian varieties; abelian integrals and differentials, Divisors, linear systems, invertible sheaves
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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 External book reviews, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Schemes and morphisms, Generalizations (algebraic spaces, stacks), Noncommutative algebraic geometry, Finite ground fields in algebraic geometry, Witt vectors and related rings, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Arithmetic varieties and schemes; Arakelov theory; heights, \(K\)-theory of schemes, Collections of articles 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 Research exposition (monographs, survey articles) pertaining to algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Rational points, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, (Equivariant) Chow groups and rings; motives, 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 Kim, M.: Remark on fundamental groups and effective Diophantine methods for hyperbolic curves. In: Goldfeld, D. et al. (eds.) Number Theory, Analysis and Geometry, pp. 355-368. Springer, New York (2012) (http://people.maths.ox.ac.uk/kimm/papers/effective.pdf) 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 Rational points, 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 Gasbarri, C.: Some topics in Arakelov theory of arithmetic surfaces, Rend. semin. Mat. univ. Politec. Torino 53, No. 3, 309-323 (1995) 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 E. V. Flynn, An explicit theory of heights , Trans. Amer. Math. Soc. 347 (1995), no. 8, 3003-3015. JSTOR: 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 Gratton, C.; Nguyen, K.; Tucker, T. J., ABC implies primitive prime divisors in arithmetic dynamics, \textit{Bull. Lond. Math. Soc.}, 45, 1194-1208, (2013) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, 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 G. Faltings, Mathematics around Kim's new proof of Siegel's theorem, Diophantine Goemetry, Proceedings of the research program at the Centro di Ricerca Matematica Ennio de Giorgi, U. Zannier (ed.), 390 pp., 2007. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Étale and other Grothendieck topologies and (co)homologies, Arithmetic problems in algebraic geometry; Diophantine 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 Chen, I, On siegel's modular curve of level 5 and the class number one problem, J. Number Theory, 74, 278-297, (1999) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Class numbers, class groups, discriminants, Elliptic curves over local fields, 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 G. S. Call and S.W. Goldstine, ''Canonical heights on projective space,'' J. Number Theory 63(2), 211--243 (1997). Arithmetic varieties and schemes; Arakelov theory; 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 Structure of families (Picard-Lefschetz, monodromy, etc.), Fibrations, degenerations in algebraic geometry, Rational and birational maps, Arithmetic varieties and schemes; Arakelov theory; heights, Integration on analytic sets and spaces, currents, Integral representations; canonical kernels (Szegő, Bergman, etc.), Residues for several complex variables
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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 Vioreanu, B. G.: Mordell-Weil problem for cubic surfaces, numerical evidence, Clay math. Proc. 8, 223-240 (2009) Varieties over global fields, Heights, Rational and ruled 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 Global theory and resolution of singularities (algebro-geometric aspects), Group actions on varieties or schemes (quotients), \(3\)-folds, Representation theory for linear algebraic groups, 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 Yoshitomi K.: On height functions on Jacobian surfaces. Manuscripta Math. 96, 37--66 (1998) Jacobians, Prym varieties, Theta functions and abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), 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 J. Shalika, R. Takloo-Bighash, Y. Tschinkel, Rational points and automorphic forms, Contributions to Automorphic Forms, Geometry, and Number Theory (H. Hida, D. Ramakrishnan, F. Shahidi, eds.), Johns Hopkins Univ. Press. (2004), 733--742. Heights, Representations of Lie and linear algebraic groups over local fields, Holomorphic modular forms of integral weight, Rational points, Varieties 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, Holomorphic modular forms of integral weight, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Modular and Shimura varieties, 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 Morrow, M., An explicit approach to residues on and dualizing sheaves of arithmetic surfaces, New York J. Math., 16, 575-627, (2010) Arithmetic varieties and schemes; Arakelov theory; heights, Ramification and extension theory, Arithmetic ground fields for curves, Local cohomology and algebraic geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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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
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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 Heights, Torsion-free groups, finite rank, Algebraic numbers; rings of algebraic integers, Algebraic theory of 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 Rational points, Varieties over global fields, Heights, Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, Dynamical systems over global ground fields, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems, Rational and birational maps
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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 [17] Randriambololona (H.).-- Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faiseaux cohérents, J. Reine Angew. Math. 590, p.~67-88 (2006). &MR~22 | &Zbl~1097. 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 Hahn, T.: An arithmetic Riemann-Roch theorem for metrics with cusps. Ph.D. dissertation, Humboldt University, (2009). Arithmetic varieties and schemes; Arakelov theory; heights, Research exposition (monographs, survey articles) pertaining to number theory, 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 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rigid analytic geometry, Fibrations, degenerations 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 T. BOREK, Successive minima and slopes of hermitian vector bundles over number fields. J. Number Theory, 113 (2) (2005), pp. 380-388. Zbl1100.14513 MR2153282 Arithmetic varieties and schemes; Arakelov theory; 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 Counting solutions of Diophantine equations, Dynamical systems over global ground fields, Heights, Algebraic numbers; rings of algebraic integers, 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 Schmidt, Alexander; Wingberg, Kay, On the fundamental group of a smooth arithmetic surface, Math. Nachr., 159, 19-36, (1992), MR 1237099 (94k:14026) Homotopy theory and fundamental groups in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Coverings of curves, fundamental group, Local ground fields in algebraic geometry, 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 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Learning and adaptive systems in artificial intelligence
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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 Frey, Gerhard; Kani, Ernst, Curves of genus \(2\) covering elliptic curves and an arithmetical application.Arithmetic algebraic geometry, Texel, 1989, Progr. Math. 89, 153-176, (1991), Birkhäuser Boston, Boston, MA Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Local ground fields in algebraic geometry, Elliptic curves 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 Weng, L., Regularized determinants of Laplacians for Hermitian line bundles over projective spaces, J. Math. Kyoto Univ., 35, 341-355, (1995) Riemann-Roch theorems, Determinantal varieties, Vector bundles on curves and their moduli, Characteristic classes and numbers in differential topology, Arithmetic varieties and schemes; Arakelov theory; heights, Sheaves and cohomology of sections of holomorphic vector bundles, general results, 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 [19] Parshin (A.~N.).-- On the application of ramified coverings in the theory of diophantine equations. Math. USSR Sbornik 60, p.~249-264 (1990). &MR~9 | &Zbl~0702. Arithmetic varieties and schemes; Arakelov theory; heights, Coverings in algebraic geometry, Arithmetic ground fields for curves, Rational points, Higher degree equations; Fermat's equation
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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 Zeta functions and \(L\)-functions of number fields, Distribution of prime ideals, Arithmetic varieties and schemes; Arakelov theory; heights, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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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 Rojas, J. M.: On the complexity of Diophantine geometry in low dimensions. (1999) Analysis of algorithms and problem complexity, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Decidability (number-theoretic aspects), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic varieties and schemes; Arakelov theory; heights, 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 Poonen, B.: Curves over every global field violating the local-global principle. Zap. Nauchn. Sem. POMI \textbf{377} (2010), Issledovaniya po Teorii Chisel \textbf{10}, 141-147, 243-244. Reprinted in: J. Math. Sci. (N.Y.) \textbf{171}, 782-785 (2010) Curves of arbitrary genus or genus \(\ne 1\) over global fields, 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 C. Soulé, ''Géométrie d'Arakelov des surfaces arithmétiques,'' Astérisque, vol. 177-178, p. exp. no. 713, 327-343, 1989. 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 Rational points, Arithmetic aspects of modular and Shimura varieties, Heights, Computer solution of Diophantine equations
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