Extensions for Finite Chevalley Groups III: Rational and Generic Cohomology

Christopher P. Bendel; Daniel K. Nakano; Cornelius Pillen

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arXiv · 1306.3385

Extensions for Finite Chevalley Groups III: Rational and Generic Cohomology

Christopher P. Bendel·Daniel K. Nakano·Cornelius Pillen

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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 $G({\mathbb F}_{q})$ are established which generalizes earlier work of Hiller, in addition to stability ranges for generic cohomology which improves on seminal work of Cline, Parshall, Scott and van der Kallen.

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BibTeX RIS

Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen. 2013-10-15. Extensions for Finite Chevalley Groups III: Rational and Generic Cohomology. https://arxiv.org/abs/1306.3385

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