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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 ground fields for abelian varieties, Elliptic and modular units, Polylogarithms and relations with \(K\)-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 Elliptic curves over global fields, Heights, Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), 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 Elliptic curves over global fields, Complex multiplication and moduli of abelian varieties, Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global 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 T. SHIODA, Existence of a rational elliptic surface with a given Mordell-Weil lattice, Proc. Japan Acad Ser. A, Math. Sci. 68 (1992), 251-255. Rational points, Elliptic curves, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and ruled surfaces, Arithmetic varieties and schemes; Arakelov theory; heights, Other nonalgebraically closed 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 B. Poonen, Sieve methods for varieties over finite fields and arithmetic schemes , J. Théor. Nombres Bordeaux 19 (2007), 221-229. Varieties over finite and local fields, Finite ground fields in algebraic geometry, 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 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Potentials and capacities on other spaces, Algebraic numbers; rings of algebraic integers, 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 [12] M.H. Hedayatzadeh, \(Exterior powers of \)\pi\(-divisible modules over fields\), J. Number Theory, 138, (2014), 119-174. &MR 31 Class field theory; \(p\)-adic formal groups, Formal groups, \(p\)-divisible 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 Borisov, A., Convolution structures and arithmetic cohomology, Compos. Math., 136, 237-254, (2003) Algebraic numbers; rings of algebraic integers, Arithmetic varieties and schemes; Arakelov theory; heights, Positive definite functions on groups, semigroups, etc., Character groups and dual objects
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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, Varieties 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 A. Bravo, E. Villamayor, Smoothness and tangent bundles of arithmetical schemes, Math. Z., to appear. Local structure of morphisms in algebraic geometry: étale, flat, etc., Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Rational and birational maps, Global theory and resolution of singularities (algebro-geometric 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 Joseph A. Shalika and Yuri Tschinkel, Height zeta functions of equivariant compactifications of the Heisenberg group, Contributions to automorphic forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD, 2004, pp. 743 -- 771. Rational points, Heights, 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 Bruin P., Explicit bounds on automorphic and canonical Green functions of Fuchsian groups, Mathematika 60 (2014), no. 2, 257-306. Spectral theory; trace formulas (e.g., that of Selberg), Modular and Shimura varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Green's functions for elliptic 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 DOI: 10.1016/j.jnt.2012.09.023 Algebraic cycles, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Finite ground fields in algebraic geometry, Subvarieties of abelian varieties, 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, Transcendental methods, Hodge theory (algebro-geometric aspects), Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Galois representations
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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, Bull. Amer. Math. Soc., n.s., 43, 139--161 (2006); arXiv:math/0502016v1 [math.AG] (2005). History of algebraic geometry, Mathematics in general, Arithmetic varieties and schemes; Arakelov theory; heights, Dimension theory in general topology, Dimension theory in algebraic topology, Congruences for modular and \(p\)-adic modular forms, Noncommutative geometry (à la Connes)
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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 dynamics on general algebraic varieties, Fractals, Arithmetic varieties and schemes; Arakelov theory; heights, Counting solutions 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 Zhang, S.: Distribution of almost division points. Duke math J 103, No. 1, 39-46 (2000) Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian 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 Saito, T.: Weight-monodromy conjecture for \(\mathcall \)-adic representations associated to modular forms. In: Gordon, B.B., Lewis, J., Müller-Stach, S., Saito, S., Yui, N (eds.) The Arithmetic and Geometry of Algebraic Cycles, pp. 427-431. Springer, New York (2000) Galois representations, Arithmetic varieties and schemes; Arakelov theory; heights, \(p\)-adic cohomology, crystalline cohomology, \(p\)-adic theory, local fields, 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 Shinya Harada and Toshiro Hiranouchi, Smallness of fundamental groups for arithmetic schemes, J. Number Theory 129 (2009), no. 11, 2702 -- 2712. Arithmetic varieties and schemes; Arakelov theory; heights, Geometric class field theory, Ramification problems in algebraic geometry, Homotopy theory and fundamental groups 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 E. Viada , Bounds for minimal elliptic isogenies . Preprint. Results involving abelian varieties, Subvarieties of abelian varieties, Heights, Counting solutions 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 M. Rapoport, Non-Archimedean period domains, in Proceedings of the International Congress of Mathematicians, vol. 1, 2 (Zürich, 1994) (Birkhäuser, Basel, 1995), pp. 423--434 Varieties over finite and local fields, Arithmetic varieties and schemes; Arakelov theory; heights, Modular and Shimura varieties, 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 Lercier, R.; Ritzenthaler, C.; Sijsling, J., Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent, (ANTS X--Proceedings of the Tenth Algorithmic Number Theory Symposium. ANTS X--Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Ser., vol. 1, (2013), Math. Sci. Publ.: Math. Sci. Publ. Berkeley, CA), 463-486 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic 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 Arithmetic varieties and schemes; Arakelov theory; heights, Cohomology theory for linear algebraic 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 David, Sinnou; Philippon, Patrice, Minorations des hauteurs normalisées des sous-variétés de variétés abéliennes.Number theory, Tiruchirapalli, 1996, Contemp. Math. 210, 333-364, (1998), Amer. Math. Soc., Providence, RI Abelian varieties of dimension \(> 1\), Arithmetic varieties and schemes; Arakelov theory; heights, Transcendence (general theory), 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 E. Aldrovandi, Hermitian-holomorphic Deligne cohomology, Deligne pairing for singu- lar metrics, and hyperbolic metrics, Int. Math. Res. Not. 2005, no. 17, 1015-1046. Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Arithmetic varieties and schemes; Arakelov theory; heights, Sheaves and cohomology of sections of holomorphic vector bundles, general results
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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 Pollack, A.: Relations between derivations arising from modular forms, Ph.D. thesis. Duke University (2009) Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), 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 B. Poonen, ''Bertini theorems over finite fields,'' Ann. of Math., vol. 160, iss. 3, pp. 1099-1127, 2004. Finite ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Projective techniques in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties, 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 Shor, Caleb M., Higher-order Weierstrass weights of branch points on superelliptic curves, (Malmendier, A.; Shaska, T., Algebraic curves and their fibrations in mathematical physics and arithmetic geometry, Contemp. math., (2017), Amer. Math. Soc.), to appear Riemann surfaces; Weierstrass points; gap sequences, 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 Transcendence (general theory), Arithmetic varieties and schemes; Arakelov theory; heights, Dynamical aspects of holomorphic foliations and vector fields, 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 Gillet, H.; Rössler, D.; Soulé, C., An arithmetic Riemann-Roch theorem in higher degrees, Ann. Inst. Fourier, 58, 6, 2169-2189, (2008) Arithmetic varieties and schemes; Arakelov theory; heights, Riemann-Roch theorems, 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 E. Schaefer, ''Computing a Selmer Group of a Jacobian Using Functions on the Curve,'' Math. Ann. 310, 447--471 (1998); ''Erratum,'' Math. Ann. 339, 1 (2007). Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Cubic and quartic 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 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), Fibrations, degenerations in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Maps between classifying spaces in algebraic topology, Stacks and moduli problems, Representation theory for linear algebraic 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, 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 Kerz, M.: Higher class field theory and the connected component Generalized class field theory (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Geometric class field 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 Algebraic functions and function fields in algebraic geometry, Galois theory, 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 Counting solutions of Diophantine equations, Asymptotic results on arithmetic functions, Arithmetic varieties and schemes; Arakelov theory; heights, Hasse principle, weak and strong approximation, Brauer-Manin obstruction, Hypersurfaces and 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 Gillet, Henri; Soulé, Christophe, Characteristic classes for algebraic vector bundles with Hermitian metric. I, Ann. of Math. (2), 131, 1, 163-203, (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Smoothing in differential topology
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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., \textit{arithmetic Hirzebruch-Zagier cycles}, J. reine angew. Math., 515, 155-244, (1999) Arithmetic aspects of modular and Shimura varieties, Fourier coefficients of automorphic forms, Heights, 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 Call, G.; Silverman, J., \textit{canonical heights on varieties with morphisms}, Compos. Math., 89, 163-205, (1993) 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 Chinburg T. , Pappas G. , Taylor M.J. , \epsilon -constants and Arakelov-Euler characteristics , Math. Res. Lett. 7 ( 2000 ) 433 - 446 . Zbl 1097.14501 Arithmetic varieties and schemes; Arakelov theory; heights, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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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 Jones, J.: P-adic heights for semi-stable abelian varieties. Compositio math. 73, 31-56 (1990) Arithmetic ground fields for abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Iwasawa theory, 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 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), 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 Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic cycles, Local ground fields in algebraic geometry, Global ground fields in algebraic geometry, 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 Heights, Model theory of ordered structures; o-minimality, Rational points, Transcendence theory of other special functions
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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 Silverman J.H.: Integer points, Diophantine approximation, and iteration of rational maps. Duke Math. J. 71(3), 793--829 (1993) Diophantine approximation, transcendental number theory, Global ground fields in algebraic geometry, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, Topological dynamics
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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 ____, Points of bounded height on equivariant compactifications of vector groups, II . J. Number Theory 85 ( 2000 ), n^\circ 2 , 172 - 188 . MR 1802710 | Zbl 0963.11034 Varieties over global fields, Rational points, 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 Loughran, D., Rational points of bounded height and the Weil restriction, Israel J. Math., 210, 1, 47-79, (2015) Rational points, Counting solutions of Diophantine equations, Heights, Applications of the Hardy-Littlewood method, Other analytic 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 T. Hibino and N. Murabayashi: Modular equations of hyperelliptic \(X_0(N)\) and an application , Acta Arith. 82 (1997), 279--291. Holomorphic modular forms of integral weight, Special algebraic curves and curves of low genus, 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 McQuillan, M., Holomorphic curves on hyperplane sections of \(3\)-folds, Geom. Funct. Anal., 9, 2, 370-392, (1999) Arithmetic ground fields for curves, \(3\)-folds, Arithmetic varieties and schemes; Arakelov theory; heights, Zero sets of holomorphic functions 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 Stoll, M., \textit{implementing 2-descent for Jacobians of hyperelliptic curves}, Acta Arithmetica, XCVIII.3, 245-277, (2001) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for curves, Jacobians, Prym varieties, Number-theoretic algorithms; complexity, 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 A.Moriwaki, Faltings modular height and self-intersection of dualizing sheaf. Preprint. Arithmetic varieties and schemes; Arakelov theory; 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 aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Families, moduli of curves (algebraic), 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 Z. Jin and M. Marcolli, Endomotives of toric varieties, J. Geom. Phys., 77 (2014), 48--71. Zbl 1315.14010 MR 3157902 (Equivariant) Chow groups and rings; motives, Toric varieties, Newton polyhedra, Okounkov bodies, Arithmetic varieties and schemes; Arakelov theory; heights, Noncommutative geometry (à la Connes), Noncommutative geometry in quantum theory, Commutation relations and statistics as related to quantum mechanics (general)
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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, Heights, 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 Exponential sums, Varieties over finite and local 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 [3]S. Arias-de-Reyna, W. Gajda, and S. Petersen, Big monodromy theorem for abelian varieties over finitely generated fields, J. Pure Appl. Algebra 217 (2013), 218--229. Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, 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 J. H. Silverman: A lower bound for the canonical height on elliptic curves over abelian extensions. J. Number Theory 104 (2004), 353--372. Elliptic curves over global fields, Abelian varieties of dimension \(> 1\), Heights, 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 McCallum, William; Poonen, Bjorn, The method of Chabauty and Coleman, explicit methods in number theory, Panor. Synthèses, vol. 36, 99-117, (2012), Soc. Math. France Paris, (English, with English and French summaries), MR3098132 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Analytic theory of abelian varieties; abelian integrals and differentials
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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 Howard, B, Complex multiplication cycles and kudla-Rapoport divisors, II, Am. J. Math., 137, 639-698, (2015) 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 C. Gasbarri,Hermitian vector bundles of rank two and adjoint systems on arithmetic surfaces, Topology38 (1999), 1161--1174. Vector bundles on surfaces and higher-dimensional varieties, and their moduli, 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 automorphic functions, Structure of modular groups and generalizations; arithmetic groups, Automorphic forms, one variable, 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 Dedekind, R.: Gesammelte mathematische Werke. Bände I-III. Herausgegeben von Robert Fricke, Emmy Noether und Öystein Ore. Chelsea Publishing Co., New York (1968) 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 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 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Isogeny
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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 aspects of modular and Shimura varieties, 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), Families, moduli of curves (algebraic), 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 J.\ L. Thunder, Asymptotic estimates for rational points of bounded height on flag varieties, Compos. Math. 88 (1993), 155-186. Arithmetic algebraic geometry (Diophantine geometry), Geometry of numbers, Grassmannians, Schubert varieties, flag manifolds, 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 Jorgenson J. and Kramer J. (2006). Non-completeness of the Arakelov-induced metric on moduli space of curves. Manusc. Math. 119: 453--463 Arithmetic varieties and schemes; Arakelov theory; heights, Families, moduli of curves (algebraic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Heat and other parabolic equation methods for PDEs on 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 Bogomolov, F., Tschinkel, Yu.: Couniformization of curves over number fields. In: Bogomolov, F., Tschinkel, Yu. (eds.) Geometric Methods in Algebra and Number Theory. Progress in Mathematics, vol.~235, pp.~43-57. Birkhäuser, Boston (2005). http://www.math.nyu.edu/~tschinke/papers/yuri/04covers/cover4.pdf 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 E.V. Flynn and N.P. Smart, Canonical heights on the Jacobians of curves of genus 2 and the infinite descent, Acta Arith., 79 (1997), 333-352. MR 98f:11066 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 Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Collections of abstracts of lectures, 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 Linear forms in logarithms; Baker's method, Transcendence theory of other special functions, Elliptic curves over local fields, 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 Kuwata, M., The canonical height and elliptic surfaces, J. Number Theory, 36, 2, 201-211, (1990), MR 1072465 Rational points, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Cubic and quartic Diophantine equations, Arithmetic varieties and schemes; Arakelov theory; heights, 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 Cossidente, A.; Korchmáros, G.; Torres, F., Curves of large genus covered by the Hermitian curve, Comm. Algebra, 28, 4707-4728, (2000) Curves over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Finite 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 N. Broberg, ''A note on a paper by R. Heath-Brown: 'The density of rational points on curves and surfaces','' J. reine angew. Math., 571, 159--178 (2004). Varieties over global fields, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Counting solutions of Diophantine equations, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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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 Howard, B, Complex multiplication cycles and kudla-Rapoport divisors, Ann. Math., 176, 1097-1171, (2012) Arithmetic varieties and schemes; Arakelov theory; heights, 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 Hoshi Y., Existence of nongeometric pro-p Galois sections of hyperbolic curves, Publ. Res. Inst. Math. Sci. 46 (2010), 829-848. Coverings of curves, fundamental group, 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 Arithmetic varieties and schemes; Arakelov theory; heights, 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 Higher degree equations; Fermat's equation, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Counting solutions of Diophantine equations, Power series rings, 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 Benedict H. Gross, Hanoi lectures on the arithmetic of hyperelliptic curves, Acta Math. Vietnam. 37 (2012), no. 4, 579 -- 588. 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 Bertrand Meyer, Generalised Hermite constants, Voronoi theory and heights on flag varieties, Bull. Soc. Math. France 137 (2009), no. 1, 127 -- 158 (English, with English and French summaries). Minima of forms, 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 Wiesend G.: Class field theory for arithmetic schemes. Math. Z. 256(4), 717--729 (2007) Arithmetic varieties and schemes; Arakelov theory; heights, Geometric class field 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 Coleman, R.; Edixhoven, B., On the semi-simplicity of the \(U_p\)-operator on modular forms, Math. Ann., 310, 1, 119-127, (1998) Congruences for modular and \(p\)-adic modular forms, 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, 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 Kudla, S.; Rapoport, M., Height pairings on Shimura curves and \textit{p}-adic uniformization, Invent. Math., 142, 153-222, (2000) Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Formal groups, \(p\)-divisible groups, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), 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 Philippon, P.; Sur des hauteurs alternatives. I; Math. Ann.: 1991; Volume 289 ,255-284. Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for abelian varieties, Abelian varieties of dimension \(> 1\), Transcendence (general theory), Algebraic numbers; rings of algebraic integers, 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 Riemann-Roch theorems, Arithmetic varieties and schemes; Arakelov theory; heights, Spectral theory; trace formulas (e.g., that of Selberg), Determinants and determinant bundles, analytic torsion, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (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 Saïdi, M.: Fake liftings of Galois covers between smooth curves. In: Galois-Teichmüller Theory and Arithmetic Geometry. Advanced Studies in Pure Mathematics, vol.~63, pp.~457--501. Mathematical Society of Japan, Tokyo (2012) Arithmetic varieties and schemes; Arakelov theory; heights, 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 Families, moduli of curves (algebraic), Coverings of curves, fundamental group, 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 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function 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 Y. Ihara, ``Horizontal divisors on arithmetic surfaces associated with Belyĭ uniformizations'' in The Grothendieck Theory of Dessins d'Enfants (Luminy, France, 1993) , London Math. Soc. Lecture Note Ser. 200 , Cambridge Univ. Press, Cambridge, 1994, 245--254. Divisors, linear systems, invertible sheaves, Homotopy theory and fundamental groups in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Special 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 Clemens Fuchs, Rafael von Känel, and Gisbert Wüstholz, An effective Shafarevich theorem for elliptic curves, Acta Arith. 148 (2011), no. 2, 189 -- 203. Elliptic curves over global fields, Cubic and quartic Diophantine equations, Algebraic moduli problems, moduli of vector bundles, 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 Valerio Talamanca, A note on height pairings on polarized abelian varieties, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat.10 (1999), p. 57-60 Algebraic theory of abelian 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 de Jong R.: Arakelov invariants of Riemann surfaces. Doc. Math. 10, 311--329 (2005) Arithmetic varieties and schemes; Arakelov theory; heights, Theta functions and curves; Schottky problem, 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 Gerd Faltings , Does there exist an arithmetic Kodaira-Spencer class? , Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), Contemp. Math. 241, American Mathematical Society, 1999, p. 141-146 Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Varieties 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 Proceedings, conferences, collections, etc. pertaining to number theory, Abelian varieties of dimension \(> 1\), Curves over finite and local fields, Varieties over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic coding theory; cryptography (number-theoretic aspects), Special algebraic curves and curves of low genus, Arithmetic ground fields for abelian varieties, Representations of finite groups of Lie type, Geometric methods (including applications of algebraic geometry) applied to coding theory, 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 Klaus Künnemann, Higher Picard varieties and the height pairing, Amer. J. Math. 118 (1996), no. 4, 781 -- 797. Picard groups, Parametrization (Chow and Hilbert schemes), 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 Terstiege, U.: Intersections of special cycles on the Shimura variety for \(GU(1,2)\). J. Reine Angew. Math. \textbf{684}, 113-164 (2013) Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Algebraic cycles
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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 Chinburg T., Pappas G., Taylor M.J., Duality and hermitian Galois module structure , to appear in the Proc. L.M.S. MR 1978570 | Zbl 1109.11053 Integral representations related to algebraic numbers; Galois module structure of rings of integers, Global ground fields in algebraic geometry, \(L\)-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 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 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Global ground fields in algebraic geometry
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