Some Motivic Remarks On The Moduli Stacks Of global G-Shtukas And Their Local Models

TL;DR

This paper investigates the motives of moduli stacks of G-shtukas and their local models, focusing on motivic invariants, Tateness, Frobenius semi-simplicity, and purity in a motivic framework.

Contribution

It introduces a motivic perspective on G-shtukas moduli stacks, providing criteria for Tateness and reformulating purity results using local models.

Findings

Criteria for mixed Tateness of local models

Discussion on semi-simplicity of Frobenius on cohomology

Motivic reformulation of purity results

Abstract

In this article we study motives corresponding to the moduli stacks of G-shtukas and their local models. In particular we deal with the question of describing their motivic fundamental invariants. As an application, we provide a criterion for mixed Tateness of the local model, and discuss the semi-simplicity of Frobenius on their cohomology. We then use the theory of local models to reformulate a purity result for these moduli stacks in the motivic context.