Cargando…
Modular forms and special cycles on Shimura curves /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2006.
|
| Colección: | Annals of mathematics studies ;
no. 161. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | JSTOR_ocn803434031 | ||
| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
| 006 | m o d | ||
| 007 | cr |n||||||||| | ||
| 008 | 050907s2006 nju ob 001 0 eng d | ||
| 040 | |a VT2 |b eng |e pn |c VT2 |d OCLCO |d OCLCQ |d N$T |d IDEBK |d E7B |d OCLCA |d JSTOR |d N$T |d OCLCE |d OCLCF |d OCLCQ |d YDXCP |d OCLCQ |d COO |d DEBBG |d OCLCQ |d UIU |d AGLDB |d DEBSZ |d OTZ |d OCLCQ |d IOG |d EZ9 |d STF |d OCLCQ |d VTS |d REC |d OCLCQ |d LVT |d UX1 |d M8D |d OCLCO |d UKAHL |d HS0 |d VLB |d UUM |d MM9 |d AJS |d OCLCQ |d OCLCO |d CNNOR |d OCLCO |d AAA |d OCLCO |d FAU |d OCLCQ |d OCLCO | ||
| 015 | |a GBA619163 |2 bnb | ||
| 016 | 7 | |a 013391724 |2 Uk | |
| 019 | |a 626042673 |a 680616881 |a 839305284 |a 978620393 |a 978880651 |a 994897515 |a 999520623 |a 1005791559 |a 1037791756 |a 1048745412 |a 1064775886 |a 1091761170 |a 1100660397 |a 1108939655 |a 1119108286 |a 1178724241 |a 1187187229 |a 1228615255 |a 1249256032 | ||
| 020 | |a 9781400837168 |q (electronic bk.) | ||
| 020 | |a 1400837162 |q (electronic bk.) | ||
| 020 | |a 1299401023 | ||
| 020 | |a 9781299401020 | ||
| 020 | |z 0691125503 | ||
| 020 | |z 9780691125503 | ||
| 020 | |z 0691125511 | ||
| 020 | |z 9780691125510 | ||
| 024 | 7 | |a 10.1515/9781400837168 |2 doi | |
| 029 | 1 | |a AU@ |b 000054189057 | |
| 029 | 1 | |a CHBIS |b 010896027 | |
| 029 | 1 | |a CHVBK |b 483396958 | |
| 029 | 1 | |a DEBBG |b BV043056514 | |
| 029 | 1 | |a DEBBG |b BV043713078 | |
| 029 | 1 | |a DEBSZ |b 44643485X | |
| 029 | 1 | |a DEBSZ |b 478275854 | |
| 029 | 1 | |a GBVCP |b 1003708307 | |
| 035 | |a (OCoLC)803434031 |z (OCoLC)626042673 |z (OCoLC)680616881 |z (OCoLC)839305284 |z (OCoLC)978620393 |z (OCoLC)978880651 |z (OCoLC)994897515 |z (OCoLC)999520623 |z (OCoLC)1005791559 |z (OCoLC)1037791756 |z (OCoLC)1048745412 |z (OCoLC)1064775886 |z (OCoLC)1091761170 |z (OCoLC)1100660397 |z (OCoLC)1108939655 |z (OCoLC)1119108286 |z (OCoLC)1178724241 |z (OCoLC)1187187229 |z (OCoLC)1228615255 |z (OCoLC)1249256032 | ||
| 037 | |a 22573/ctt3120jw |b JSTOR | ||
| 042 | |a dlr | ||
| 050 | 4 | |a QA242.5 |b .K83 2006eb | |
| 072 | 7 | |a MAT |x 012010 |2 bisacsh | |
| 072 | 7 | |a MAT037000 |2 bisacsh | |
| 082 | 0 | 4 | |a 516.3/5 |2 22 |
| 084 | |a SK 240 |2 rvk | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Kudla, Stephen S., |d 1950- | |
| 245 | 1 | 0 | |a Modular forms and special cycles on Shimura curves / |c Stephen S. Kudla, Michael Rapoport, Tonghai Yang. |
| 260 | |a Princeton : |b Princeton University Press, |c 2006. | ||
| 300 | |a 1 online resource (vii, 373 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies ; |v no. 161 | |
| 504 | |a Includes bibliographical references and index. | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 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-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 | ||
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a Arithmetical algebraic geometry. | |
| 650 | 0 | |a Shimura varieties. | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 6 | |a Variétés de Shimura. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Shimura varieties |2 fast | |
| 650 | 7 | |a Arithmetische Geometrie |2 gnd | |
| 650 | 7 | |a Eisenstein-Reihe |2 gnd | |
| 650 | 7 | |a Shimura-Kurve |2 gnd | |
| 650 | 7 | |a Thetafunktion |2 gnd | |
| 700 | 1 | |a Rapoport, M., |d 1948- | |
| 700 | 1 | |a Yang, Tonghai, |d 1963- | |
| 776 | 0 | 8 | |i Print version: |a Kudla, Stephen S., 1950- |t Modular forms and special cycles on Shimura curves. |d Princeton : Princeton University Press, 2006 |z 0691125503 |w (DLC) 2005054621 |w (OCoLC)61500117 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 161. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt32bc0s |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH28126620 | ||
| 938 | |a ebrary |b EBRY |n ebr10678788 | ||
| 938 | |a EBSCOhost |b EBSC |n 563767 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis25154167 | ||
| 938 | |a YBP Library Services |b YANK |n 10406264 | ||
| 994 | |a 92 |b IZTAP | ||