English

Inverting Integers in Tambara Functors

Group Theory 2026-01-27 v2 Algebraic Topology Representation Theory

Abstract

Let GG be a finite group, and kk an integer. In this note, we show that for any GG-Tambara functor TT and any subgroups H1,H2GH_1, H_2 \leq G, kk is a unit in T(G/H1)T(G/H_1) if and only if kk is a unit in T(G/H2)T(G/H_2). In other words, one may speak unambiguously of the localization T[1/k]T[1/k]. As a consequence, the norm functors NHGN_H^G commute with inverting kk.

Cite

@article{arxiv.2510.25891,
  title  = {Inverting Integers in Tambara Functors},
  author = {Ben Spitz},
  journal= {arXiv preprint arXiv:2510.25891},
  year   = {2026}
}

Comments

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

R2 v1 2026-07-01T07:12:42.330Z