English

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.

Keywords

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

R2 v1 2026-06-28T12:56:08.514Z