On the number of rational points of classifying stacks for Chevalley group schemes

TL;DR

This paper calculates the number of rational points of classifying stacks for Chevalley group schemes using advanced cohomological methods, and derives related zeta functions, contributing to algebraic geometry and number theory.

Contribution

It introduces a method to compute rational points of classifying stacks for Chevalley groups via the Lefschetz-Grothendieck trace formula, providing new explicit formulas.

Findings

Derived explicit formulas for rational points of classifying stacks

Established connections between rational points and zeta functions

Applied Behrend's trace formula to algebraic stacks

Abstract

We compute the number of rational points of classifying stacks of Chevalley group schemes using the Lefschetz-Grothendieck trace formula of Behrend for $\ell$-adic cohomology of algebraic stacks. From this we also derive associated zeta functions for these classifying stacks.