Periods in equivariant and motivic contexts

TL;DR

This paper introduces a new notion of period as a multiplicative invariant in symmetric monoidal infinity-categories, explores its properties, and applies it to equivariant and motivic homotopy theories, including tt-geometry.

Contribution

It defines the period in the context of infinity-categories and demonstrates its applications in equivariant and motivic homotopy theories, expanding the understanding of tt-geometry.

Findings

Defined the period as a multiplicative characteristic in infinity-categories

Analyzed properties and examples of the period in various contexts

Applied the concept to isotropic points in motivic tt-geometry

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.)