Rigidity for equivariant pseudo pretheories

TL;DR

This paper extends classical rigidity theorems to the equivariant setting, applying to various equivariant cohomology theories and algebraic structures with finite group actions.

Contribution

It introduces equivariant versions of the Suslin and Gabber rigidity theorems for pseudo pretheories on smooth schemes with finite group actions.

Findings

Proves equivariant rigidity theorems for algebraic K-theory and related theories.

Establishes foundational results for equivariant motivic cohomology.

Provides examples including equivariant algebraic K-theory and Bredon motivic cohomology.

Abstract

We prove versions of the Suslin and Gabber rigidity theorems in the setting of equivariant pseudo pretheories of smooth schemes over a field with an action of a finite group. Examples include equivariant algebraic $K$-theory, presheaves with equivariant transfers, equivariant Suslin homology, and Bredon motivic cohomology.