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Book Title
Modular Forms & Special Cycles on Shimura Curves
ISBN
9780691125510
Publication Name
Modular Forms and Special Cycles on Shimura Curves. (Am-161)
Item Length
9.1in
Publisher
Princeton University Press
Publication Year
2006
Series
Annals of Mathematics Studies
Type
Textbook
Format
Perfect
Language
English
Item Height
0.9in
Author
Michael Rapoport, Stephen S. Kudla, Tonghai Yang
Item Width
6.1in
Item Weight
19 Oz
Number of Pages
392 Pages

關於產品

Product Information

"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-Soul? 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.

Product Identifiers

Publisher
Princeton University Press
ISBN-10
0691125511
ISBN-13
9780691125510
eBay Product ID (ePID)
48643527

Product Key Features

Author
Michael Rapoport, Stephen S. Kudla, Tonghai Yang
Publication Name
Modular Forms and Special Cycles on Shimura Curves. (Am-161)
Format
Perfect
Language
English
Publication Year
2006
Series
Annals of Mathematics Studies
Type
Textbook
Number of Pages
392 Pages

Dimensions

Item Length
9.1in
Item Height
0.9in
Item Width
6.1in
Item Weight
19 Oz

Additional Product Features

Series Volume Number
161
Lc Classification Number
Qa242.5.K83 2006
Reviews
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., "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, "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, 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 Content
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
Copyright Date
2006
Topic
Functional Analysis, Geometry / Algebraic
Lccn
2005-054621
Dewey Decimal
516.3/5
Intended Audience
College Audience
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics

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