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Modular Curves and Abelian Varieties

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  • © 2004

Overview

Editors:
  1. John E. Cremona

    1. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

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  2. Joan-Carles Lario

    1. Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, Spain

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  3. Jordi Quer

    1. Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, Spain

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  4. Kenneth A. Ribet

    1. Department of Mathematics, University of California, Berkeley, USA

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  • Includes recent contributions on modular curves and their Jacobians as well as such seminal works as Kenneth Ribet's article "Abelian varieties over the rationals and modular forms", Elisabeth Pyle's 1995 dissertation on abelian varieties over the rationals with large endomorphism algebras, and Noam Elkies' 1993 manuscript on elliptic k-curves

Part of the book series: Progress in Mathematics (PM, volume 224)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
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  2. Stable Reduction of Modular Curves

    • Irene I. Bouw, Stefan Wewers
    Pages 1-22

  3. On p-adic Families of Automorphic Forms

    • Kevin Buzzard
    Pages 23-44

  4. ℚ-curves and Abelian Varieties of GL2-type from Dihedral Genus 2 Curves

    • Gabriel Cardona
    Pages 45-52

  5. The old Subvariety of J0 (NM)

    • János A. Csirik
    Pages 53-74

  6. Irreducibility of Galois Actions on Level 1 Siegel Cusp Forms

    • Luis V. Dieulefait
    Pages 75-80

  7. On Elliptic K-curves

    • Noam D. Elkies
    Pages 81-91

  8. ℚ-Curves and Galois Representations

    • Jordan S. Ellenberg
    Pages 93-103

  9. On the Local Behavior of Ordinary Modular Galois Representations

    • Eknath Ghate
    Pages 105-124

  10. Arithmetic of ℚ-Curves

    • Josep González, Joan-Carles Lario, Jordi Quer
    Pages 125-139

  11. Serre’s Conjecture for mod 7 Galois Representations

    • Jayanta Manoharmayum
    Pages 141-149

  12. Pairings in the Arithmetic of Elliptic Curves

    • Barry Mazur, Karl Rubin
    Pages 151-163

  13. Explicit Parametrizations of Ordinary and Supersingular Regions of X 0 (p n)

    • Ken McMurdy
    Pages 165-179

  14. Elliptic ℚ-Curves with Complex Multiplication

    • Tetsuo Nakamura
    Pages 181-187

  15. Abelian Varieties over ℚ with Large Endomorphism Algebras and Their Simple Components over \( \overline Q\)

    • Elisabeth E. Pyle
    Pages 189-239

  16. Abelian Varieties over Q and Modular Forms

    • Kenneth A. Ribet
    Pages 241-261

  17. Shimura Curves Embedded in Igusa’s Threefold

    • Victor Rotger
    Pages 263-276

  18. Shafarevich-Tate Groups of Nonsquare Order

    • William A. Stein
    Pages 277-289

  19. Back Matter

    Pages 291-292
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Keywords

Editors and Affiliations

  • School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    John E. Cremona

  • Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, Spain

    Joan-Carles Lario, Jordi Quer

  • Department of Mathematics, University of California, Berkeley, USA

    Kenneth A. Ribet

Bibliographic Information

  • Book Title: Modular Curves and Abelian Varieties

  • Editors: John E. Cremona, Joan-Carles Lario, Jordi Quer, Kenneth A. Ribet

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7919-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 2004

  • Hardcover ISBN: 978-3-7643-6586-8Published: 23 February 2004

  • Softcover ISBN: 978-3-0348-9621-4Published: 23 October 2012

  • eBook ISBN: 978-3-0348-7919-4Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VIII, 289

  • Topics: Number Theory, Algebraic Geometry

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