A Note On Two Fiber Bundles and The Manifestations Of "Shtuka"

TL;DR

This paper offers a new perspective on the moduli stacks of global G-shtukas, unifying various moduli spaces through a fibered family approach and exploring local models and Hecke operations.

Contribution

It introduces a unifying interpretation of moduli stacks for G-shtukas and Higgs bundles as fibers of a family, along with a relative local model theory and motivic Hecke operations.

Findings

Unified view of moduli stacks as fibers of a family.

Development of a relative local model theory.

Analysis of motivic Hecke operations.

Abstract

In this note we intend to look at the moduli stacks for global $G$-shtukas from a new perspective. We discuss a unifying interpretation of several moduli spaces (stacks) including moduli of global $G$-shtukas and (a variant of the) moduli of Higgs bundles. We view these spaces (stacks) as different fibers of a family over a scheme (stack) locally of finite type. We discuss (a relative version of) the local model theory for this family. We also consider the Hecke stacks over the moduli stack of $G$-shtukas and discuss the corresponding (motivic) Hecke operations.