Topological comparison theorems for Bredon motivic cohomology

TL;DR

This paper proves equivariant versions of the Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology, linking algebraic and topological invariants for varieties with group actions.

Contribution

It establishes equivariant versions of a major conjecture in motivic cohomology, extending the understanding of algebraic-topological invariant relationships.

Findings

Identifies equivariant motivic and topological invariants in many degrees

Proves equivariant Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology

Applies to smooth complex and real varieties with group actions

Abstract

We prove equivariant versions of the Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology of smooth complex and real varieties with an action of the group of order two. This identifies equivariant motivic and topological invariants in a large range of degrees.