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170329 ||| eng |
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|a 9781400837168
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|a Kudla, Stephen S.
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|a Modular Forms and Special Cycles on Shimura Curves. (AM-161)
|h Elektronische Ressource
|c Stephen S. Kudla, Michael Rapoport, Tonghai Yang
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|a Course Book
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| 260 |
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|a Princeton, N.J.
|b Princeton University Press
|c 2006, [2006]©2006
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| 300 |
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|a online resource 384 pages
|b illustrations
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| 653 |
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|a Mathematik
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| 653 |
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|a Shimura-Kurve
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|a Thetafunktion
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|a MATHEMATICS / Functional Analysis
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| 653 |
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|a Shimura varieties
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|a MATHEMATICS / Geometry / Algebraic
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|a Analysis
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| 653 |
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|a Shimura, Variétés de
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| 653 |
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|a Eisenstein-Reihe
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| 653 |
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|a Arithmetical algebraic geometry
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| 653 |
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|a Géométrie algébrique arithmétique
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| 653 |
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|a Mathematics
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| 653 |
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|a Arithmetische Geometrie
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| 700 |
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|a Rapoport, Michael
|e [author]
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| 700 |
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|a Yang, Tonghai
|e [author]
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|a eng
|2 ISO 639-2
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| 989 |
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|b GRUYMPG
|a DeGruyter MPG Collection
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| 490 |
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|a Annals of Mathematics Studies
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| 500 |
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|a Mode of access: Internet via World Wide Web
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| 028 |
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|a 10.1515/9781400837168
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|t Princeton eBook Package Backlist 2000-2013
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| 773 |
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|t Princeton Univ. Press eBook Package 2000-2013
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|t Princeton eBook Package Backlist 2000-2014
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| 773 |
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|t Princeton Annals of Mathematics Backlist eBook Package
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|u https://www.degruyter.com/doi/book/10.1515/9781400837168
|x Verlag
|3 Volltext
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|a 516.3/5
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|a 516.3/5
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|a 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
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