Functor homology over an additive category
Algebraic Topology
2022-11-08 v3 K-Theory and Homology
Representation Theory
Abstract
We uncover several general phenomenas governing functor homology over additive categories. In particular, 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.2111.09719,
title = {Functor homology over an additive category},
author = {Aurélien Djament and Antoine Touzé},
journal= {arXiv preprint arXiv:2111.09719},
year = {2022}
}