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Detecting Rational Cohomology of Algebraic Groups
Author(s) -
Cline Edward T.,
Parshall Brian J.,
Scott Leonard L.
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-28.2.293
Subject(s) - cline (biology) , mathematics , library science , mathematics education , algebra over a field , computer science , sociology , pure mathematics , demography , population
Let G be a connected, semisimple algebraic group defined over an algebraically closed field k of positive characteristic p. Assume that G is defined and split over the prime field k0 = GF (p), and for q = p , let G(q) be the subgroup of GF (g)-rational points. Let V be a rational G-module, and, for a non-negative integer r, let V(r) be the rational G-module obtained by 'twisting' the original G-action on V by the r-th power of the Frobenius endomorphism a of G. In [5] we showed (together with W. van der Kallen) that, if V is finite dimensional and n is a non-negative integer, for sufficiently large m and r (depending on V and n), there are isomorphisms