Integral models of moduli spaces of shtukas with deep Bruhat-Tits level structures

TL;DR

This paper constructs integral models for moduli spaces of shtukas with deep Bruhat-Tits level structures, providing a framework that generalizes existing models and includes the Drinfeld case, with favorable geometric properties.

Contribution

It introduces a new method to embed and construct integral models of shtukas with deep Bruhat-Tits levels, extending previous work and unifying various cases.

Findings

Integral models with proper, surjective, and generically étale maps

Existence of a natural Newton stratification

Recovery of Drinfeld shtukas with Drinfeld level structures

Abstract

We construct integral models for moduli spaces of shtukas with deep Bruhat-Tits level structures. We embed the moduli space of global shtukas for a deep Bruhat-Tits group scheme into the limit of the moduli spaces of shtukas for all associated parahoric group schemes. Its schematic image defines an integral model of the moduli space of shtukas with deep Bruhat-Tits level with favourable properties: They admit proper, surjective and generically \'etale level maps as well as a natural Newton stratification. In the Drinfeld case, this general construction of integral models recovers the moduli space of Drinfeld shtukas with Drinfeld level structures.