Automorphic forms and Shimura varieties of PGSp (2) /:
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 re...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; US Office, Hackensack, NJ :
World Scientific Pub.,
©2005.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xi, 324 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 311-319) and index. |
| ISBN: | 9812703322 9789812703323 1281899267 9781281899262 |
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| 245 | 1 | 0 | |a Automorphic forms and Shimura varieties of PGSp (2) / |c by Yuval Z. Flicker. |
| 260 | |a Singapore ; |a US Office, Hackensack, NJ : |b World Scientific Pub., |c ©2005. | ||
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| 588 | 0 | |a Print version record. | |
| 520 | |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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| author | Flicker, Yuval Z. (Yuval Zvi), 1955- |
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| author_facet | Flicker, Yuval Z. (Yuval Zvi), 1955- |
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| contents | Lifting autonomic forms of PGSp(2) to PGL(4) -- Zeta functions of Shimura varieties of PGSp(2) -- Background. |
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| id | ZDB-4-EBA-ocm76964452 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:15:59Z |
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| isbn | 9812703322 9789812703323 1281899267 9781281899262 |
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| spelling | Flicker, Yuval Z. (Yuval Zvi), 1955- https://id.oclc.org/worldcat/entity/E39PBJbWyQQwrG9ccVqhRJkdQq http://id.loc.gov/authorities/names/n82071071 Automorphic forms and Shimura varieties of PGSp (2) / by Yuval Z. Flicker. Singapore ; US Office, Hackensack, NJ : World Scientific Pub., ©2005. 1 online resource (xi, 324 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 311-319) and index. Lifting autonomic forms of PGSp(2) to PGL(4) -- Zeta functions of Shimura varieties of PGSp(2) -- Background. Print version record. 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. Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Shimura varieties. http://id.loc.gov/authorities/subjects/sh93007485 Symplectic groups. http://id.loc.gov/authorities/subjects/sh85131552 Functions, Zeta. http://id.loc.gov/authorities/subjects/sh85052354 Formes automorphes. Variétés de Shimura. Groupes symplectiques. Fonctions zêta. MATHEMATICS Complex Analysis. bisacsh Automorphic forms fast Functions, Zeta fast Shimura varieties fast Symplectic groups fast Print version: Flicker, Yuval Z. (Yuval Zvi), 1955- Automorphic forms and Shimura varieties of PGSp (2). Singapore ; US Office, Hackensack, NJ : World Scientific Pub., ©2005 9812564039 (DLC) 2006274952 (OCoLC)70107204 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=174555 Volltext |
| spellingShingle | Flicker, Yuval Z. (Yuval Zvi), 1955- Automorphic forms and Shimura varieties of PGSp (2) / Lifting autonomic forms of PGSp(2) to PGL(4) -- Zeta functions of Shimura varieties of PGSp(2) -- Background. Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Shimura varieties. http://id.loc.gov/authorities/subjects/sh93007485 Symplectic groups. http://id.loc.gov/authorities/subjects/sh85131552 Functions, Zeta. http://id.loc.gov/authorities/subjects/sh85052354 Formes automorphes. Variétés de Shimura. Groupes symplectiques. Fonctions zêta. MATHEMATICS Complex Analysis. bisacsh Automorphic forms fast Functions, Zeta fast Shimura varieties fast Symplectic groups fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85010451 http://id.loc.gov/authorities/subjects/sh93007485 http://id.loc.gov/authorities/subjects/sh85131552 http://id.loc.gov/authorities/subjects/sh85052354 |
| 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 | Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Shimura varieties. http://id.loc.gov/authorities/subjects/sh93007485 Symplectic groups. http://id.loc.gov/authorities/subjects/sh85131552 Functions, Zeta. http://id.loc.gov/authorities/subjects/sh85052354 Formes automorphes. Variétés de Shimura. Groupes symplectiques. Fonctions zêta. MATHEMATICS Complex Analysis. bisacsh Automorphic forms fast Functions, Zeta fast Shimura varieties fast Symplectic groups fast |
| topic_facet | Automorphic forms. Shimura varieties. Symplectic groups. Functions, Zeta. Formes automorphes. Variétés de Shimura. Groupes symplectiques. Fonctions zêta. MATHEMATICS Complex Analysis. Automorphic forms Functions, Zeta Shimura varieties Symplectic groups |
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