Periods in equivariant and motivic contexts

Abstract

We define the period as a multiplicative characteristic of stably symmetric monoidal $\infty$-categories, develop its basic properties, and study many examples, with a focus on `ordinary' equivariant and motivic homotopy theory. We apply the findings to isotropic points in motivic tt-geometry. (Includes an appendix by Ivo Dell'Ambrogio on generalized comparison maps in tt-geometry, and an appendix by the author and Sam K. Miller on the periodic locus for derived permutation modules.)

arXiv comment50 pages, including appendix by Ivo Dell'Ambrogio; v2: new appendix by the author and Sam K. Miller proving conjecture from v1