Cohomology of Algebraic Groups with Coefficients in Twisted Representations

  • Antoine Touzé
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)


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 90s. 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.

2010 Mathematics Subject Classification

Primary 20G10 Secondary 18G15 



The author thanks the anonymous referee for very carefully reading a first version of the article and detecting several mistakes.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Laboratoire Painlevé, Cité Scientifique - Bâtiment M2Université Lille 1 - Sciences et TechnologiesVilleneuve d’Ascq CedexFrance

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