Homology of strict polynomial functors over Fp-linear additive categories

Aurélien Djament; Antoine Touzé

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arXiv · 2407.10502

Homology of strict polynomial functors over Fp-linear additive categories

Aurélien Djament·Antoine Touzé

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Abstract

We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they open the way to new applications to stable homology of groups or to K-theory. As an illustration, we prove comparison theorems between cohomologies of classical algebraic groups over infinite perfect fields, in the spirit of a celebrated result of Cline, Parshall, Scott et van der Kallen for finite fields.

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BibTeX RIS

Aurélien Djament, Antoine Touzé. 2024-07-15. Homology of strict polynomial functors over Fp-linear additive categories. https://arxiv.org/abs/2407.10502

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