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Progress in Mathematics

By: John Cremona (Editor), Joan-Carles Lario (Editor), Jordi Quer (Editor)

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Hardcover | 23 February 2004

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304 Pages

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23.5 x 15.88 x 2.54

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It would be difficult to overestimate the influence and importance of modular forms, modular curves, and modular abelian varieties in the development of num ber theory and arithmetic geometry during the last fifty years. These subjects lie at the heart of many past achievements and future challenges. For example, the theory of complex multiplication, the classification of rational torsion on el liptic curves, the proof of Fermat's Last Theorem, and many results towards the Birch and Swinnerton-Dyer conjecture all make crucial use of modular forms and modular curves. A conference was held from July 15 to 18, 2002, at the Centre de Recerca Matematica (Bellaterra, Barcelona) under the title "Modular Curves and Abelian Varieties". Our conference presented some of the latest achievements in the theory to a diverse audience that included both specialists and young researchers. We emphasized especially 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 abelian varieties of dimension larger than one (abelian varieties of GL2-type).

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Non-Fiction Mathematics Groups & Group Theory Number Theory Geometry Algebraic Geometry Algebra

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Published: 23rd October 2012

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Stable reduction of modular curves	p. 1
On p-adic families of automorphic forms	p. 23
Q-curves and abelian varieties of GL[subscript 2]-type from dihedral genus 2 curves	p. 45
The old subvariety of J[subscript 0](NM)	p. 53
Irreducibility of Galois actions on level 1 Siegel cusp forms	p. 75
On elliptic k-curves	p. 81
Q-curves and Galois representations	p. 93
On the local behaviour of ordinary modular Galois representations	p. 105
Arithmetic of Q-curves	p. 125
Serre's conjecture for mod 7 Galois representations	p. 141
Pairings in the arithmetic of elliptic curves	p. 151
Explicit parametrizations of ordinary and supersingular regions of X[subscript 0](p[superscript n])	p. 165
Elliptic Q-curves with complex multiplication	p. 181
Abelian varieties over Q with large endomorphism algebras and their simple components over Q	p. 189
Abelian varieties over Q and modular forms	p. 241
Shimura curves embedded in Igusa's threefold	p. 263
Shafarevich-Tate groups of nonsquare order	p. 277
Table of Contents provided by Blackwell. All Rights Reserved.

Progress in Mathematics

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Hardcover

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You Can Find This Book In

Other Editions and Formats

Paperback

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