Homology of strict polynomial functors over Fp-linear additive categories

TL;DR

This paper extends a key theorem in functor homology to Fp-linear additive categories, enabling new computations and applications in algebraic K-theory and group cohomology.

Contribution

It generalizes the strong comparison theorem to a broader categorical setting, facilitating explicit functor homology calculations and new applications.

Findings

Comparison theorems for cohomologies of algebraic groups over infinite fields

Enhanced methods for explicit functor homology computations

New insights into stable homology and K-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.