On actions of Frobenius morphisms for moduli stacks of principal bundles over algebraic curves

TL;DR

This paper investigates the actions of Frobenius morphisms on the moduli stack of principal bundles over algebraic curves, explicitly describing their effects on $ ext{ell}$-adic cohomology via Chern classes.

Contribution

It provides an explicit description of Frobenius actions on the cohomology of moduli stacks of principal bundles, linking arithmetic and geometric aspects.

Findings

Explicit formulas for Frobenius actions on cohomology

Connection between Frobenius morphisms and Chern classes

Enhanced understanding of arithmetic geometry of moduli stacks

Abstract

We study the various arithmetic and geometric Frobenius morphisms on the moduli stack of principal bundles over a smooth projective algebraic curve and determine explicitly their actions on the $\ell-$adic cohomology of the moduli stack in terms of Chern classes.