1. Separable commutative algebras in equivariant homotopy theory
- Author
-
Naumann, Niko, Pol, Luca, and Ramzi, Maxime
- Subjects
Mathematics - Algebraic Topology - Abstract
Given a finite group $G$ and a commutative ring $G$-spectrum $R$, we study the separable commutative algebras in the category of compact $R$-modules. We isolate three conditions on the geometric fixed points of $R$ which ensure that every separable commutative algebra is standard, i.e. arises from a finite $G$-set. In particular we show that all separable commutative algebras in the categories of compact objects in $G$-spectra and in derived $G$-Mackey functors are standard provided that $G$ is a $p$-group. In these categories we also show that for a general finite group $G$, we cannot expect all separable commutative algebras to be standard., Comment: 26 pages
- Published
- 2024