Adeles and Algebraic Groups
Published on 2. June 2012
Book
Paperback/Softback
VI, 126 pages
978-1-4684-9158-6 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1982
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Illustrations
VI, 126 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
224 gr
ISBN-13
978-1-4684-9158-6 (9781468491586)
DOI
10.1007/978-1-4684-9156-2
Schweitzer Classification
Other editions
Additional editions
J. Coates
Adeles and Algebraic Groups
Book
01/1982
Birkhauser Boston Inc
€89.13
Article exhausted; check different version
Content
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.