Modular Forms and Special Cycles on Shimura Curves
Language: English
Published by Princeton University Press, 2006
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
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£ 141.67
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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.…
Seller Inventory # 9780691125510
- Title
- Modular Forms and Special Cycles on Shimura Curves
- Author
- Stephen S. Kudla
- Publisher
- Princeton University Press
- Publication year
- 2006
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 0691125511
- ISBN 13
- 9780691125510
- Item weight
- 588 grams
- Dimensions
- 234x156x21 mm
- Series
- Book 10 of 202: Annals of Mathematics Studies
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