Arithmetic Algebraic Geometry

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 à Nultiplications Réelles.-Séries de Kronecker et Fonctions L des Puissances Symétriques 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 Naïve Point of View.-Polylogarithms, Dedekind Zeta Functions, and the Algebraic K-Theory of Fields.-Finiteness Theorems for Dimensions of Irreducible lambda-adic Representations.