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Adeles and Algebraic Groups
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Kataloginformation
Feldname
Details
Dewey Class
512.7
Titel
Adeles and Algebraic Groups ([EBook]) / by A. Weil.
Verfasser
Weil, André , 1906-1998
Other name(s)
SpringerLink (Online service)
Veröffentl
Boston, MA : Birkhäuser , 1982.
Physical Details
VI, 126 pages : online resource.
Reihe
Progress in mathematics
0743-1643 ; ; 23
ISBN
9781468491562
Summary Note
This volume contains the original lecture notes presented by A. Weil in which the concept of adeles was first introduced, in conjunction with various aspects of C.L. Siegel’s work on quadratic forms. These notes have been supplemented by an extended bibliography, and by Takashi Ono’s brief survey of subsequent research. Serving as an introduction to the subject, these notes may also provide stimulation for further research.:
Contents note
I. Preliminaries on Adele-Geometry -- 1.1. Adeles -- 1.2. Adele-spaces attached to algebraic varieties -- 1.3. Restriction of the basic field -- II. Tamagawa Measures -- 2.1. Preliminaries -- 2.2. The case of an algebraic variety: the local measure -- 2.3. The global measure and the convergence factors -- 2.4. Algebraic groups and Tamagawa numbers -- III. The Linear, Projective and Symplectic Groups -- 3.1. The zeta-function of a central division algebra -- 3.2. The projective group of a central division algebra -- 3.3. Isogenies -- 3.4. End of proof of Theorem 3.3.1.: central simple algebras -- 3.5. The symplectic group -- 3.6. Isogenies for products of linear groups -- 3.7. Application to some orthogonal and hermitian groups -- 3.8. The zeta-function of a central simple algebra -- IV. The other Classical Groups -- 4.1. Classification and general theorems -- 4.2. End of proof of Theorem 4.1.3 (types 01, L2(a), S2) -- 4.3. The local zeta-functions for a quadratic form -- 4.4. The Tamagawa number (hermitian and quaternionic cases) -- 4.5. The Tamagawa number of the orthogonal group -- Appendix 2. (by T. Ono) A short survey of subsequent research on Tamagawa numbers.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4684-9156-2
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Schlagwörter:
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Algebraic Geometry
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Group theory
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Group Theory and Generalizations
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K-Theory
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Lie groups
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Mathematics
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Number Theory
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Topological groups
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Topological groups, Lie groups
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Authors:
Weil, André 1906-1998
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Weil, André, 1906-1998
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Corporate Authors:
SpringerLink (Online service)
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Series:
Progress in mathematics
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Classification:
512.7
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