Compactification of Level Maps of Moduli Spaces of Drinfeld Shtukas

TL;DR

This paper introduces Drinfeld level structures for shtukas of any rank, demonstrating that their moduli spaces are regular and possess finite flat level maps, leading to improved integral models and compactifications.

Contribution

It defines new Drinfeld level structures for shtukas and proves the regularity and flatness of their moduli spaces, enhancing the understanding of their geometric properties.

Findings

Moduli spaces of Drinfeld shtukas with level structures are regular.

These spaces admit finite flat level maps.

They provide good integral models and compactifications.

Abstract

We define Drinfeld level structures for Drinfeld shtukas of any rank and show that their moduli spaces are regular and admit finite flat level maps. In particular, the moduli spaces of Drinfeld shtukas with Drinfeld $\Gamma_0(\mathfrak{p}^n)$-level structures provide a good integral model and relative compactification of the moduli space of shtukas with naive $\Gamma_0(\mathfrak{p}^n)$-level defined using shtukas for dilated group schemes.