arXiv:2407.10502 [math.AT]AbstractReferencesReviewsResources
Homology of strict polynomial functors over Fp-linear additive categories
Aurélien Djament, Antoine Touzé
Published 2024-07-15Version 1
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.
Comments: This preprint reworks a part of the material of our previous preprint ''Functor homology over an additive category'' (hal-03432824 or arXiv:2111.09719), which is being completely reorganized. 48 pages
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