Author | Weil, A. author |
---|---|
Title | Adeles and Algebraic Groups [electronic resource] / by A. Weil |
Imprint | Boston, MA : Birkhรคuser Boston, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9156-2 |
Descript | VI, 126 p. online resource |
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