Extensions for finite Chevalley groups III: Rational and generic cohomology |
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Authors: | Christopher P. Bendel Daniel K. Nakano Cornelius Pillen |
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Affiliation: | 1. Department of Mathematics, Statistics and Computer Science, University of Wisconsin-Stout, Menomonie, WI 54751, USA;2. Department of Mathematics, University of Georgia, Athens, GA 30602, USA;3. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA |
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Abstract: | Let G be a connected reductive algebraic group and B be a Borel subgroup defined over an algebraically closed field of characteristic p>0. In this paper, the authors study the existence of generic G-cohomology and its stability with rational G-cohomology groups via the use of methods from the authors' earlier work. New results on the vanishing of G and B -cohomology groups are presented. Furthermore, vanishing ranges for the associated finite group cohomology of G(Fq) are established which generalize earlier work of Hiller, in addition to stability ranges for generic cohomology which improve on seminal work of Cline, Parshall, Scott and van der Kallen. |
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Keywords: | 20J06 20G10 |
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