Homology of strict polynomial functors over Fp-linear additive categories
Algebraic Topology
2024-07-16 v1 Category Theory
Group Theory
K-Theory and Homology
Representation Theory
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.
Cite
@article{arxiv.2407.10502,
title = {Homology of strict polynomial functors over Fp-linear additive categories},
author = {Aurélien Djament and Antoine Touzé},
journal= {arXiv preprint arXiv:2407.10502},
year = {2024}
}
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