Lecture Notes Prepared in Connection with the Summer Institute on Algebraic Groups and Discontinuous Subgroups Held at the University of Colorado, Boulder, Colorado, July 5-August 6, 1965

摘要

The principal developments in the arithmetic aspects of algebraic groups are included in the following five major topics: Algebraic linear groups and arithmetic groups, including a survey of the structure and classification theory over arbitrary fields, groups over Z, the maximal compact subgroups of p-adic groups, and reduction theory for arithmetic groups. Adelization, Tamagawa numbers, the Siegel-Weil formula, Galois cohomology, and approximation theorems. Automorphic forms, the spectral decomposition of L-squared (G/gamma), Eisenstein series, interpretation of a Ramanujan conjecture. The compactification and projective imbedding of arithmetically defined quotients of bounded symmetric domains, partial desingularization of the compactification, fiber systems of polarized abelian varieties, fields of moduli, zeta-functions, theta-functions, L-functions, Fourier-Jacobi series, symplectic representations. Vector-valued cohomology and rigidity theorems. (Author)