Arithmetic algebraic geometry
Author(s)
Bibliographic Information
Arithmetic algebraic geometry
（Progress in mathematics, v. 89）
Birkhäuser, 1991
- : sz
- : us
Available at / 81 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
C||Arithmetic-290093855
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:510/G2712070174967
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Note
"The conference Arithmetic Algebraic Geometry, Texel'89, which was held on Texel Island during the last week of April 1989" -- p. vii
Includes bibliographies
Description and Table of Contents
Description
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.
Table of Contents
Participants.-Contributors.-Introduction.-Well-Adjusted Models for Curves over Dedekind Rings.-On the Manin Constants of Modular Elliptic Curves.-The Action of Monogromy on Torsion Points of Jacobians.-An Exceptional Isomorphism between Modular Varieties.-Chern Functors.-Curves of Genus 2Covering Elliptic Curves and an Arithmetical Application.-Jacobians with Complex Multiplication.-Familles de Courbes Hyperelliptiques a Nultiplications Reelles.-Series de Kronecker et Fonctions L des Puissances Symetriques de Courbes Elliptiques sur Q.-Hyperelliptic Supersingular Curves.-Letter to Don Zagier.-The Old Subvariety of J(pq).-Loyvagin's System of Gauss Sums.-The Exponents of the Groups of Points on the Reductions of an Elliptic Curve.-The Generalized De Rham-Witt Complex and Congruence Differential Equations.-Arithmetic Discriminants and Quadratic Points on Curves.-The Birch-Swinnerton-Dyer Conjecture from a Naive Point of View.-Polylogarithms, Dedekind Zeta Functions, and the Algebraic K-Theory of Fields.-Finiteness Theorems for Dimensions of Irreducible lambda-adic Representations.
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