On the Chow Ring of the Classifying Space of some Chevalley Groups

TL;DR

This paper computes the Chow ring of the classifying space for certain Chevalley groups over finite fields and extends the results to complex numbers via specialization, advancing understanding in algebraic geometry and group theory.

Contribution

It introduces a method to compute the Chow ring of classifying spaces of Chevalley groups over finite fields and extends these results to complex numbers through specialization techniques.

Findings

Chow rings of specific Chevalley groups are explicitly computed.

Results are extended from characteristic p to complex numbers.

Provides new tools for studying algebraic groups and their classifying spaces.

Abstract

Let $p$ be a prime and $q$ be a power of $p$. We compute the Chow ring of the classifying space of some Chevalley groups $G(\mathbb{F}_q)$, when considered as a finite algebraic group over a field of characteristic $p$ containing $\mathbb{F}_q$. Using specialization from characteristic $0$ to characteristic $p$ we also obtain results over the complex numbers.