On the rational $C_2$-homotopy type of ${BSU_{\mathbb{R}}}_m$

TL;DR

This paper describes the rational $C_2$-equivariant homotopy type of the classifying space ${BSU_{ eal}}_m$ using equivariant Eilenberg-MacLane spaces, addressing a problem in motivic homotopy theory.

Contribution

It provides a new description of the rational $C_2$-homotopy type of ${BSU_{ eal}}_m$, linking motivic homotopy theory with equivariant homotopy theory.

Findings

Rational $C_2$-homotopy type of ${BSU_{ eal}}_m$ characterized.

Description in terms of equivariant Eilenberg-MacLane spaces.

Addresses a problem posed by Asok-Fasel-Hopkins.

Abstract

Motivated by a problem in motivic homotopy theory considered by Asok-Fasel-Hopkins, we give a description of the rational $C_2$-equivariant homotopy type of the classifying space ${BSU_{\mathbb{R}}}_m$ in terms of equivariant Eilenberg-Maclane spaces.