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arXiv · 2005.14106

Finite generation of cohomology for Drinfeld doubles of finite group schemes

Cris Negron
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Abstract

We prove that the Drinfeld double of an arbitrary finite group scheme has finitely generated cohomology. That is to say, for G any finite group scheme, and D(G) the Drinfeld double of the group ring kG, we show that the self-extension algebra of the trivial representation for D(G) is a finitely generated algebra, and that for each D(G)-representation V the extensions from the trivial representation to V form a finitely generated module over the aforementioned algebra. As a corollary, we find that all categories rep(G)*_M dual to rep(G) are of also of finite type (i.e. have finitely generated cohomology), and we provide a uniform bound on their Krull dimensions. This paper completes earlier work of E. M. Friedlander and the author.

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Cris Negron. 2020-05-28. Finite generation of cohomology for Drinfeld doubles of finite group schemes. https://arxiv.org/abs/2005.14106

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