Automorphic forms and Shimura varieties of PGSp (2):
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific Pub.
c2005
|
| Subjects: | |
| Online Access: | DE-1046 DE-1047 Volltext |
| Item Description: | Includes bibliographical references (p. 311-319) and index Lifting autonomic forms of PGSp(2) to PGL(4) -- Zeta functions of Shimura varieties of PGSp(2) -- Background The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings." This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ) in SL(4, ). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture |
| Physical Description: | 1 Online-Ressource (xi, 324 p.) |
| ISBN: | 1281899267 9781281899262 9789812703323 9812703322 |
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MARC
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| 500 | |a The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings." This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ) in SL(4, ). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture | ||
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| 650 | 7 | |a Automorphic forms |2 fast | |
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| 650 | 4 | |a Shimura varieties | |
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Record in the Search Index
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| adam_text | |
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| author | Flicker, Yuval Z., (Yuval Zvi) |
| author_facet | Flicker, Yuval Z., (Yuval Zvi) |
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| author_sort | Flicker, Yuval Z., (Yuval Zvi) |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV043083714 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-30T12:00:29Z |
| institution | BVB |
| isbn | 1281899267 9781281899262 9789812703323 9812703322 |
| language | English |
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| spelling | Flicker, Yuval Z., (Yuval Zvi) Verfasser aut Automorphic forms and Shimura varieties of PGSp (2) by Yuval Z. Flicker Singapore World Scientific Pub. c2005 1 Online-Ressource (xi, 324 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 311-319) and index Lifting autonomic forms of PGSp(2) to PGL(4) -- Zeta functions of Shimura varieties of PGSp(2) -- Background The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings." This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ) in SL(4, ). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture MATHEMATICS / Complex Analysis bisacsh Automorphic forms fast Functions, Zeta fast Shimura varieties fast Symplectic groups fast Automorphic forms Shimura varieties Symplectic groups Functions, Zeta Projektive Gruppe (DE-588)4175885-7 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Symplektische Gruppe (DE-588)4276585-7 gnd rswk-swf Projektive Gruppe (DE-588)4175885-7 s 1\p DE-604 Automorphe Form (DE-588)4003972-9 s 2\p DE-604 Symplektische Gruppe (DE-588)4276585-7 s 3\p DE-604 Shimura-Mannigfaltigkeit (DE-588)4181143-4 s 4\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=174555 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Flicker, Yuval Z., (Yuval Zvi) Automorphic forms and Shimura varieties of PGSp (2) MATHEMATICS / Complex Analysis bisacsh Automorphic forms fast Functions, Zeta fast Shimura varieties fast Symplectic groups fast Automorphic forms Shimura varieties Symplectic groups Functions, Zeta Projektive Gruppe (DE-588)4175885-7 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Automorphe Form (DE-588)4003972-9 gnd Symplektische Gruppe (DE-588)4276585-7 gnd |
| subject_GND | (DE-588)4175885-7 (DE-588)4181143-4 (DE-588)4003972-9 (DE-588)4276585-7 |
| title | Automorphic forms and Shimura varieties of PGSp (2) |
| title_auth | Automorphic forms and Shimura varieties of PGSp (2) |
| title_exact_search | Automorphic forms and Shimura varieties of PGSp (2) |
| title_full | Automorphic forms and Shimura varieties of PGSp (2) by Yuval Z. Flicker |
| title_fullStr | Automorphic forms and Shimura varieties of PGSp (2) by Yuval Z. Flicker |
| title_full_unstemmed | Automorphic forms and Shimura varieties of PGSp (2) by Yuval Z. Flicker |
| title_short | Automorphic forms and Shimura varieties of PGSp (2) |
| title_sort | automorphic forms and shimura varieties of pgsp 2 |
| topic | MATHEMATICS / Complex Analysis bisacsh Automorphic forms fast Functions, Zeta fast Shimura varieties fast Symplectic groups fast Automorphic forms Shimura varieties Symplectic groups Functions, Zeta Projektive Gruppe (DE-588)4175885-7 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Automorphe Form (DE-588)4003972-9 gnd Symplektische Gruppe (DE-588)4276585-7 gnd |
| topic_facet | MATHEMATICS / Complex Analysis Automorphic forms Functions, Zeta Shimura varieties Symplectic groups Projektive Gruppe Shimura-Mannigfaltigkeit Automorphe Form Symplektische Gruppe |
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