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    Modular Curves and Abelian Varieties (Progress in Mathematics) (Hardback) Edited by John Cremona, Edited by Joan-Carles Lario, Edited by Jordi Quer, Edited by Kenneth Ribet

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    DescriptionIt 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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    Title
    Modular Curves and Abelian Varieties
    Authors and contributors
    Edited by John Cremona, Edited by Joan-Carles Lario, Edited by Jordi Quer, Edited by Kenneth Ribet
    Physical properties
    Format: Hardback
    Number of pages: 304
    Width: 156 mm
    Height: 234 mm
    Thickness: 17 mm
    Weight: 603 g
    Language
    English
    ISBN
    ISBN 13: 9783764365868
    ISBN 10: 3764365862
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    LC subject heading:
    B&T Modifier: Region of Publication: 01
    B&T Merchandise Category: SCI
    B&T General Subject: 710
    B&T Modifier: Academic Level: 02
    Ingram Subject Code: MA
    BISAC V2.8: MAT002000
    LC subject heading:
    Warengruppen-Systematik des deutschen Buchhandels: 16230
    BIC subject category V2: PBMW
    LC subject heading:
    BISAC V2.8: MAT022000, MAT012010
    LC subject heading:
    DC22: 516.3/53, 516.353
    Libri: ZAHL3000
    LC subject heading: ,
    LC classification: QA567.2.M63 M63 2004, QA1-939, QA241-247.5, QA564-609
    Edition statement
    2004 ed.
    Illustrations note
    biography
    Publisher
    Birkhauser Verlag AG
    Imprint name
    Birkhauser Verlag AG
    Publication date
    27 May 2004
    Publication City/Country
    Basel
    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.