num_pages: 126
description: 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 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.
language: English
title: Adeles and Algebraic Groups
titlecomplete: Adeles and Algebraic Groups (Progress in Mathematics)
ratings_count: 1
publisher: Birkhauser