Google full text of our books:


Modular Forms and Special Cycles on Shimura Curves. (AM-161)
Stephen S. Kudla, Michael Rapoport, & Tonghai Yang

Paperback | 2006 | $97.00 | ($58.20) / £67.00 | (£40.20) | ISBN: 9780691125510
392 pp. | 6 x 9 | 1 line illus. 3 tables.
Add to Shopping Cart

eBook | ISBN: 9781400837168 |
Our eBook editions are available from these online vendors

Reviews | Table of Contents
Chapter 1[PDF] pdf-icon

Google full text of this book:

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.


"This book represents a major milestone for research at the intersection of arithmetic geometry and automorphic forms. The results will shape the research in this area for some time to come."--Jens Funke, Mathematical Reviews

Table of Contents:

Acknowledgments ix
Chapter 1. Introduction 1
Bibliography 21
Chapter 2. Arithmetic intersection theory on stacks 27
Chapter 3. Cycles on Shimura curves 45
Chapter 4. An arithmetic theta function 71
Chapter 5. The central derivative of a genus two Eisenstein series 105
Chapter 6. The generating function for 0-cycles 167
Chapter 6 Appendix. The case p = 2, p | D (B) 181
Chapter 7. An inner product formula 205
Chapter 8. On the doubling integral 265
Chapter 9. Central derivatives of L-functions 351
Index 371

Another Princeton book authored or coauthored by Michael Rapoport:


Subject Area:


Shopping Cart:

  • For ebooks:

Our eBook editions are available
from these online vendors:

  • Amazon Kindle Store
  • Google Play eBook Store
  • Intel Education Study eBook Store
  • Many of our ebooks are available through
    library electronic resources including these platforms:

  • Books at JSTOR
  • Ebrary
  • Ebook Library
  • EBSCO Ebooks
  • MyiLibrary
  • Dawsonera (UK)

  • For hardcover/paperback orders in United States, Canada, Latin America, Asia, and Australia

     Paperback $97.00 | ($58.20) ISBN: 9780691125510

    Add to shopping cart
    View contents of your shopping cart

    For hardcover/paperback orders in Europe, Africa, the Middle East, India, and Pakistan

     Paperback £67.00 | (£40.20) ISBN: 9780691125510

    Add to shopping cart
    View contents of your shopping cart

    Prices subject to change without notice

    File created: 11/20/2015

    Questions and comments to:
    Princeton University Press

    fall saleHoliday Sale
    New Book E-mails
    New In Print
    PUP Blog
    Princeton APPS
    Sample Chapters
    Princeton Legacy Library
    Exam/Desk Copy
    Recent Awards
    Princeton Shorts
    Freshman Reading
    PUP Europe
    About Us
    Contact Us
    PUP Home

    Bookmark and Share
    Send me emails
    about new books in:
    More Choices