Homology of strict polynomial functors over Fp-linear additive categories

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Djament, Aurélien, Touzé, Antoine
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866929421177323520
author Djament, Aurélien
Touzé, Antoine
author_facet Djament, Aurélien
Touzé, Antoine
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_10502
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Homology of strict polynomial functors over Fp-linear additive categories
Djament, Aurélien
Touzé, Antoine
Algebraic Topology
Category Theory
Group Theory
K-Theory and Homology
Representation Theory
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.
title Homology of strict polynomial functors over Fp-linear additive categories
topic Algebraic Topology
Category Theory
Group Theory
K-Theory and Homology
Representation Theory
url https://arxiv.org/abs/2407.10502