The homology of additive functors in prime characteristic
K-Theory and Homology
2026-03-10 v3
Abstract
We compute certain Ext and Tor groups in the category of all functors from an Z/p-linear additive category A to vector spaces in terms of Ext and Tor computed in the full subcategory of additive functors from A to vector spaces. We thus obtain group homology computations for general linear groups.
Cite
@article{arxiv.2407.10522,
title = {The homology of additive functors in prime characteristic},
author = {Aurélien Djament and Antoine Touzé},
journal= {arXiv preprint arXiv:2407.10522},
year = {2026}
}
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