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Modular Forms and Special Cycles on Shimura Curves. (AM-161) /
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 fu...
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| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2006.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 006 | m o d | ||
| 007 | cr||||||||nn|n | ||
| 008 | 050907s2006 nju o 00 0 eng d | ||
| 020 | |a 9781400837168 | ||
| 020 | |z 9780691125510 | ||
| 020 | |z 9780691125503 | ||
| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Kudla, Stephen S., |d 1950- | |
| 245 | 1 | 0 | |a Modular Forms and Special Cycles on Shimura Curves. (AM-161) / |c Stephen S. Kudla, Michael Rapoport, Tonghai Yang. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2006. | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 0000 | |
| 264 | 4 | |c ©2006. | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Annals of mathematics studies ; |v no. 161 | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Acknowledgments -- |t Chapter 1. Introduction -- |t Chapter 2. Arithmetic intersection theory on stacks -- |t Chapter 3. Cycles on Shimura curves -- |t Chapter 4. An arithmetic theta function -- |t Chapter 5. The central derivative of a genus two Eisenstein series -- |t Chapter 6. The generating function for 0-cycles -- |t Chapter 6 Appendix -- |t Chapter 7. An inner product formula -- |t Chapter 8. On the doubling integral -- |t Chapter 9. Central derivatives of L-functions -- |t Index. |
| 520 | |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-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 | ||
| 546 | |a In English. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 0 | 7 | |a Thetafunktion. |2 swd |
| 650 | 0 | 7 | |a Shimura-Kurve. |2 swd |
| 650 | 0 | 7 | |a Eisenstein-Reihe. |2 swd |
| 650 | 0 | 7 | |a Arithmetische Geometrie. |2 swd |
| 650 | 7 | |a Thetafunktion |2 gnd | |
| 650 | 7 | |a Shimura-Kurve |2 gnd | |
| 650 | 7 | |a Eisenstein-Reihe |2 gnd | |
| 650 | 7 | |a Arithmetische Geometrie |2 gnd | |
| 650 | 7 | |a Shimura varieties. |2 fast |0 (OCoLC)fst01116007 | |
| 650 | 7 | |a Arithmetical algebraic geometry. |2 fast |0 (OCoLC)fst00814526 | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 6 | |a Varietes de Shimura. | |
| 650 | 6 | |a Geometrie algebrique arithmetique. | |
| 650 | 0 | |a Shimura varieties. | |
| 650 | 0 | |a Arithmetical algebraic geometry. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 700 | 1 | |a Yang, Tonghai, |d 1963- | |
| 700 | 1 | |a Rapoport, M., |d 1948- | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/33476/ |
| 945 | |a Project MUSE - Custom Collection | ||