Cohomology of algebraic groups with coefficients in twisted representations

2018/10/03 by Antoine Touzé, Touzé, Antoine · 1 citation
Mathematics · #20G10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:20G10

paper · pdf · doi:10.48550/arxiv.1810.01631

32 pages. To appear in Geometric and Topological Aspects of Group Representations, eds. JF Carlson, SB Iyengar and J Pevtsova, PIMS (2018), Springer

arxiv created 2018/10/03 · openalex publication_date 2018/10/03 · arxiv updated 2018/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtained by the theory of strict polynomial functors initiated by Friedlander and Suslin in the late nineties. The last section explains that the existence of certain `universal classes' used to prove cohomological finite generation is equivalent to some recent `untwisting theorems' in the theory of strict polynomial functors. We actually provide thereby a new proof of these theorems.

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• Ext-group in the category of quantum polynomial functors via the quantum Frobenius twist

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