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Item Details
| Title:
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MODULAR FORMS AND SPECIAL CYCLES ON SHIMURA CURVES. (AM-161)
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| By: |
Stephen S. Kudla, Michael Rapoport, Tonghai Yang |
| Format: |
Paperback |
| List price:
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£95.00 |
| Our price: |
£76.00 |
| Discount: |
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| You save:
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£19.00 |
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| ISBN 10: |
0691125511 |
| ISBN 13: |
9780691125510 |
| Availability: |
Usually dispatched within 1-3 weeks.
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| Stock: |
Currently 0 available |
| Publisher: |
PRINCETON UNIVERSITY PRESS |
| Pub. date: |
4 April, 2006 |
| Series: |
Annals of Mathematics Studies |
| Pages: |
392 |
| Description: |
A 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. |
| Synopsis: |
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-Soule 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. |
| Illustrations: |
1 line illus. 3 tables. |
| Publication: |
US |
| Imprint: |
Princeton University Press |
| Returns: |
Returnable |
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