Modular Forms and Special Cycles on Shimura Curves. (AM-161) / / Stephen S. Kudla, Tonghai Yang, Michael Rapoport.
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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Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2006] ©2006 |
Year of Publication: | 2006 |
Edition: | Course Book |
Language: | English |
Series: | Annals of Mathematics Studies ;
161 |
Online Access: | |
Physical Description: | 1 online resource (392 p.) :; 1 line illus. 3 tables. |
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LEADER | 08445nam a22019815i 4500 | ||
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001 | 9781400837168 | ||
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020 | |a 9781400837168 | ||
024 | 7 | |a 10.1515/9781400837168 |2 doi | |
035 | |a (DE-B1597)446524 | ||
035 | |a (OCoLC)979577404 | ||
040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
041 | 0 | |a eng | |
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050 | 4 | |a QA242.5 |b .K83 2006eb | |
072 | 7 | |a MAT037000 |2 bisacsh | |
082 | 0 | 4 | |a 516.3/5 |2 22 |
100 | 1 | |a Kudla, Stephen S., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Modular Forms and Special Cycles on Shimura Curves. (AM-161) / |c Stephen S. Kudla, Tonghai Yang, Michael Rapoport. |
250 | |a Course Book | ||
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2006] | |
264 | 4 | |c ©2006 | |
300 | |a 1 online resource (392 p.) : |b 1 line illus. 3 tables. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 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 |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Arithmetical algebraic geometry. | |
650 | 0 | |a Géométrie algébrique arithmétique. | |
650 | 0 | |a Shimura varieties. | |
650 | 0 | |a Shimura, Variétés de. | |
650 | 7 | |a MATHEMATICS / Functional Analysis. |2 bisacsh | |
653 | |a Abelian group. | ||
653 | |a Addition. | ||
653 | |a Adjunction formula. | ||
653 | |a Algebraic number theory. | ||
653 | |a Arakelov theory. | ||
653 | |a Arithmetic. | ||
653 | |a Automorphism. | ||
653 | |a Bijection. | ||
653 | |a Borel subgroup. | ||
653 | |a Calculation. | ||
653 | |a Chow group. | ||
653 | |a Coefficient. | ||
653 | |a Cohomology. | ||
653 | |a Combinatorics. | ||
653 | |a Compact Riemann surface. | ||
653 | |a Complex multiplication. | ||
653 | |a Complex number. | ||
653 | |a Cup product. | ||
653 | |a Deformation theory. | ||
653 | |a Derivative. | ||
653 | |a Dimension. | ||
653 | |a Disjoint union. | ||
653 | |a Divisor. | ||
653 | |a Dual pair. | ||
653 | |a Eigenfunction. | ||
653 | |a Eigenvalues and eigenvectors. | ||
653 | |a Eisenstein series. | ||
653 | |a Elliptic curve. | ||
653 | |a Endomorphism. | ||
653 | |a Equation. | ||
653 | |a Explicit formulae (L-function). | ||
653 | |a Fields Institute. | ||
653 | |a Formal group. | ||
653 | |a Fourier series. | ||
653 | |a Fundamental matrix (linear differential equation). | ||
653 | |a Galois group. | ||
653 | |a Generating function. | ||
653 | |a Green's function. | ||
653 | |a Group action. | ||
653 | |a Induced representation. | ||
653 | |a Intersection (set theory). | ||
653 | |a Intersection number. | ||
653 | |a Irreducible component. | ||
653 | |a Isomorphism class. | ||
653 | |a L-function. | ||
653 | |a Laurent series. | ||
653 | |a Level structure. | ||
653 | |a Line bundle. | ||
653 | |a Local ring. | ||
653 | |a Mathematical sciences. | ||
653 | |a Mathematics. | ||
653 | |a Metaplectic group. | ||
653 | |a Modular curve. | ||
653 | |a Modular form. | ||
653 | |a Modularity (networks). | ||
653 | |a Moduli space. | ||
653 | |a Multiple integral. | ||
653 | |a Number theory. | ||
653 | |a Numerical integration. | ||
653 | |a Orbifold. | ||
653 | |a Orthogonal complement. | ||
653 | |a P-adic number. | ||
653 | |a Pairing. | ||
653 | |a Prime factor. | ||
653 | |a Prime number. | ||
653 | |a Pullback (category theory). | ||
653 | |a Pullback (differential geometry). | ||
653 | |a Pullback. | ||
653 | |a Quadratic form. | ||
653 | |a Quadratic residue. | ||
653 | |a Quantity. | ||
653 | |a Quaternion algebra. | ||
653 | |a Quaternion. | ||
653 | |a Quotient stack. | ||
653 | |a Rational number. | ||
653 | |a Real number. | ||
653 | |a Residue field. | ||
653 | |a Riemann zeta function. | ||
653 | |a Ring of integers. | ||
653 | |a SL2(R). | ||
653 | |a Scientific notation. | ||
653 | |a Shimura variety. | ||
653 | |a Siegel Eisenstein series. | ||
653 | |a Siegel modular form. | ||
653 | |a Special case. | ||
653 | |a Standard L-function. | ||
653 | |a Subgroup. | ||
653 | |a Subset. | ||
653 | |a Summation. | ||
653 | |a Tensor product. | ||
653 | |a Test vector. | ||
653 | |a Theorem. | ||
653 | |a Three-dimensional space (mathematics). | ||
653 | |a Topology. | ||
653 | |a Trace (linear algebra). | ||
653 | |a Triangular matrix. | ||
653 | |a Two-dimensional space. | ||
653 | |a Uniformization. | ||
653 | |a Valuative criterion. | ||
653 | |a Whittaker function. | ||
700 | 1 | |a Rapoport, Michael, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
700 | 1 | |a Yang, Tonghai, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Backlist 2000-2013 |z 9783110442502 |
776 | 0 | |c print |z 9780691125510 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9781400837168 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400837168 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400837168/original |
912 | |a 978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013 |c 2000 |d 2013 | ||
912 | |a EBA_BACKALL | ||
912 | |a EBA_CL_MTPY | ||
912 | |a EBA_EBACKALL | ||
912 | |a EBA_EBKALL | ||
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