The Chow Ring of the 2-Sylow Subgroup of $\mathrm{GL}(4,2)$

TL;DR

This paper computes the mod 2 Chow ring of the classifying space of the 2-Sylow subgroup of GL(4,2), providing a general, automatable method for similar computations in algebraic geometry.

Contribution

It introduces a largely automated strategy for computing Chow rings of motivic étale classifying spaces, demonstrated on a specific finite group.

Findings

Computed the mod 2 Chow ring of the Sylow 2-subgroup of GL(4,2)

Developed a general, automatable computation strategy

Facilitated quicker calculations for similar algebraic structures

Abstract

This paper provides a computation of the mod 2 Chow ring of the motivic \'etale classifying space of the finite group $\mathrm{Syl}_2(\mathrm{GL}(4,2))$. It outlines a general computation strategy, adapted from work by Burt Totaro, that has been largely automated by the author. This strategy can be used to compute more examples of Chow rings of motivic \'etale classifying spaces quickly.