On the vanishing ranges for the cohomology of finite groups of Lie type II

2011/12/11 by Christopher P. Bendel, Bendel, Christopher P., Daniel K. Nakano +3
Mathematics · #20G10 #20J06 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20G10 #msc:20J06

paper · pdf · doi:10.48550/arxiv.1112.2367

arxiv created 2011/12/11 · openalex publication_date 2011/12/11 · arxiv updated 2011/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The computation of the cohomology for finite groups of Lie type in the describing characteristic is a challenging and difficult problem. In earlier work, the authors constructed an induction functor which takes modules over the finite group of Lie type to modules for the ambient algebraic group G. In particular this functor when applied to the trivial module yields a natural G-filtration. This filtration was utilized in the earlier work to determine the first non-trivial cohomology class when the underlying root system is of type A_n or C_n. In this paper the authors extend these results toward locating the first non-trivial cohomology classes for the remaining finite groups of Lie type (i.e., the underlying root system is of type B_n, C_n, D_n, E₆, E₇, E₈, F₄, and G₂) when the prime is larger than the Coxeter number.

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