Inverting Integers in Tambara Functors

Abstract

Let $G$ be a finite group, and $k$ an integer. In this note, we show that for any $G$-Tambara functor $T$ and any subgroups $H_1,H_2\le G$, $k$ is a unit in $T(G/H_1)$ if and only if $k$ is a unit in $T(G/H_2)$. In other words, one may speak unambiguously of the localization $T[1/k]$. As a consequence, the norm functors $N_H^G$ commute with inverting $k$.

9 pages, final version (to appear in Proceedings of the AMS)