Periods in equivariant and motivic contexts

We define the period as a multiplicative characteristic of stably symmetric monoidal $\mathrm{\infty }$-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.)