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  • © 2004

Modular Curves and Abelian Varieties

Birkhäuser
  • 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
  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. The old Subvariety of J0 (NM)

    • János A. Csirik
    Pages 53-74
  5. On Elliptic K-curves

    • Noam D. Elkies
    Pages 81-91
  6. ℚ-Curves and Galois Representations

    • Jordan S. Ellenberg
    Pages 93-103
  7. Arithmetic of ℚ-Curves

    • Josep González, Joan-Carles Lario, Jordi Quer
    Pages 125-139
  8. Serre’s Conjecture for mod 7 Galois Representations

    • Jayanta Manoharmayum
    Pages 141-149
  9. Pairings in the Arithmetic of Elliptic Curves

    • Barry Mazur, Karl Rubin
    Pages 151-163
  10. Elliptic ℚ-Curves with Complex Multiplication

    • Tetsuo Nakamura
    Pages 181-187
  11. Abelian Varieties over Q and Modular Forms

    • Kenneth A. Ribet
    Pages 241-261
  12. Shafarevich-Tate Groups of Nonsquare Order

    • William A. Stein
    Pages 277-289
  13. Back Matter

    Pages 291-292

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

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access