Compactification of Level Maps of Moduli Spaces of Drinfeld Shtukas

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 $Γ_0(\mathfrak{p}^n)$-level structures provide a good integral model and relative compactification of the moduli space of shtukas with naive $Γ_0(\mathfrak{p}^n)$-level defined using shtukas for dilated group schemes.