The homology of additive functors in prime characteristic

TL;DR

This paper develops methods to compute Ext and Tor groups for functors in prime characteristic, enabling new group homology calculations for general linear groups.

Contribution

It introduces a framework to relate Ext and Tor computations in the entire functor category to those in the subcategory of additive functors, advancing homology calculations.

Findings

Computed Ext and Tor groups for functors in prime characteristic

Derived group homology results for general linear groups

Established relations between functor categories and homological algebra

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.