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Modular Curves and Abelian Varieties

✍ Scribed by Irene I. Bouw, Stefan Wewers (auth.), John E. Cremona, Joan-Carles Lario, Jordi Quer, Kenneth A. Ribet (eds.)

Publisher
BirkhΓ€user Basel
Year
2004
Tongue
English
Leaves
290
Series
Progress in Mathematics 224
Edition
1
Category
Library
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✦ Synopsis

This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca MatemοΏ½ tica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.

✦ Table of Contents

Front Matter....Pages i-viii
Stable Reduction of Modular Curves....Pages 1-22
On p -adic Families of Automorphic Forms....Pages 23-44
β„š-curves and Abelian Varieties of GL 2 -type from Dihedral Genus 2 Curves....Pages 45-52
The old Subvariety of J 0 (NM )....Pages 53-74
Irreducibility of Galois Actions on Level 1 Siegel Cusp Forms....Pages 75-80
On Elliptic K -curves....Pages 81-91
β„š-Curves and Galois Representations....Pages 93-103
On the Local Behavior of Ordinary Modular Galois Representations....Pages 105-124
Arithmetic of β„š-Curves....Pages 125-139
Serre’s Conjecture for mod 7 Galois Representations....Pages 141-149
Pairings in the Arithmetic of Elliptic Curves....Pages 151-163
Explicit Parametrizations of Ordinary and Supersingular Regions of X 0 ( p n )....Pages 165-179
Elliptic β„š-Curves with Complex Multiplication....Pages 181-187
Abelian Varieties over β„š with Large Endomorphism Algebras and Their Simple Components over $$ \overline Q$$ ....Pages 189-239
Abelian Varieties over Q and Modular Forms....Pages 241-261
Shimura Curves Embedded in Igusa’s Threefold....Pages 263-276
Shafarevich-Tate Groups of Nonsquare Order....Pages 277-289
Back Matter....Pages 291-292

✦ Subjects

Number Theory; Algebraic Geometry

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