Homotopical operadic calculus in positive characteristic
Algebraic Topology
2023-12-11 v2 Category Theory
Abstract
Algebraic operads provide a powerful tool to understand the homotopy theory of the types of (co)algebras they encode. So far, the principal results and methods that this theory provides were only available in characteristic zero. The reason is that operads carry an action of all the symmetric groups, whose representation theory becomes much more involved in positive characteristic. The goal of this paper is to extend these results and methods to a positive characteristic setting. We solve the main problems that appear in this new setting by using the notion of a quasi-planar cooperad as the building block of the theory.
Cite
@article{arxiv.2310.13095,
title = {Homotopical operadic calculus in positive characteristic},
author = {Brice Le Grignou and Victor Roca i Lucio},
journal= {arXiv preprint arXiv:2310.13095},
year = {2023}
}
Comments
125 pages. Minor improvements. Added results in section 2. Comments are still welcome