Modular Curves and Abelian Varieties

by John Cremona (Editor), Joan-Carles Lario (Editor), Jordi Quer (Editor), Kenneth Ribet (Editor)

Overview

This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matem 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.

Product Details

ISBN-13:	9783764365868
Publisher:	Birkh�user Basel
Publication date:	05/27/2004
Series:	Progress in Mathematics , #224
Edition description:	2004
Pages:	289
Product dimensions:	6.40(w) x 9.30(h) x 1.00(d)

Table of Contents

Stable reduction of modular curves.- On p-adic families of automorphic forms.-—-curves and abelian varieties of GL2-type from dihedral genus 2 curves.- The old subvariety of J0(NM).- Irreducibility of Galois actions on level 1 Siegel cusp forms.- On elliptic K-curves.-—-curves and Galois representations.- On the local behaviour of ordinary modular Galois representations.- Arithmetic of—-curves.- Serre’s conjecture for mod 7 Galois representations.- Pairings in the arithmetic of elliptic curves.- Explicit parametrizations of ordinary and supersingular regions of X0(Pn).- Elliptic—-curves with complex multiplication.- Abelian varieties over— with large endomorphism algebras and their simple components over—.- Abelian varieties over— and modular forms.- Shimura curves embedded in Igusa’s threefold.- Shafarevich-Tate groups of nonsquare order.