Modular curves and Abelian varieties

John Cremona, Joan-Carles Lario, Jordi Quer, Kenneth Ribet - Collection Progress in Mathematics

290 pages, parution le 09/03/2004

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Résumé

This book contains seventeen articles about GaloTs representations, modular forms, modular curves, and modular abelian varieties -subjects that have played a central role in the development of number theory and arithmetic geometry during the last fifty years. Most contributions discuss current research achievements originating from lectures of a conference on "Modular Curves and Abelian Varieties" that was held in July, 2002, at the Centre de Recerca Matematica (Bellaterra) in Barcelona. The emphasis lies on the conjectural generalization of the Shimura-Taniyama conjecture to elliptic curves over number fields other than the field of rational numbers (elliptic Q-curves) and on abelian varieties of dimension larger than 1 (abelian varieties of GL2-type). Additionally, several key articles on the subject are included that do not correspond to conference lectures. The book is intended for graduate students and young researchers as well as for specialists.

Sommaire

IRENE I. Bouw AND STEFAN WEWERS - Stable reduction of modular curves
KEVIN BUZZARD - On p-adic families of automorphic forms
GABRIEL CARDONA - Q-curves and abelian varieties of GL2-type from dihedral genus 2 curves
JANOS A. CSIRIK - The old subvariety of J0(NM) .
LUIS V. DlEULEFAIT - Irreducibility of Galois actions on level 1 Siegel cusp forms
NOAM D. ELKIES - On elliptic fc-curves
JORDAN S. ELLENBERG - Q-curves and Galois representations
EKNATH GHATE - On the local behaviour of ordinary modular Galois representations
JOSEP GONZALEZ, JOAN-CARLES LARIO AND JORDI QUER - Arithmetic of Q-curves
JAYANTA MANOHARMAYUM - Serre's conjecture for mod 7 Galois representations
BARRY MAZUR AND KARL RUBIN - Pairings in the arithmetic of elliptic curves
KEN MCMURDY - Explicit parametrizations of ordinary and supersingular regions of Xo(pn)
TETSUO NAKAMURA - Elliptic Q-curves with complex multiplication
ELISABETH E. PYLE - Abelian varieties over Q with large endomorphism algebras and their simple components over Q
KENNETH A. RIBET - Abelian varieties over Q and modular forms
VICTOR ROTGER - Shimura curves embedded in Igusa's threefold
WILLIAM A. STEIN - Shafarevich-Tate groups of nonsquare order

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	John Cremona, Joan-Carles Lario, Jordi Quer, Kenneth Ribet
Collection	Progress in Mathematics
Parution	09/03/2004
Nb. de pages	290
Format	16 x 24
Couverture	Relié
Poids	644g
Intérieur	Noir et Blanc
EAN13	3783764365864