Algebraic Groups and Number Theory
Academic Press, Dec 7, 1993 - Mathematics - 614 pages
This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
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abelian adele algebraic groups algebraic number field arbitrary arithmetic groups arithmetic subgroup assertion automorphism Borel subgroup cl(G class number cocycle cohomology commutative completes the proof congruence subgroup conjecture conjugate connected group consider contains Corollary corresponding decomposition defined denote element equivalent exact sequence exists extension L/K finite index finite number finite subset follows fundamental set Gal(L/K Galois extension GLn(R group G groups of type Haar measure Hasse principle hence homomorphism integer involution isomorphism K-group K-group G K-split K-torus kernel lattice Lemma Let G matrix Moreover morphism normal subgroup Note obtain proof of Proposition proof of Theorem prove quadratic extension quadratic form quasisplit reductive respect root satisfying semisimple groups simple simply connected skew field strong approximation subgroup of G suffices suitable surjective theory topology torus trivial unipotent unramified valuation variety weak approximation