Integral Models of Moduli Spaces of Shtukas with Deep Level Structures

We construct integral models for moduli spaces of shtukas with deep Bruhat-Tits level structures. In the Drinfeld case, 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 space of Drinfeld shtukas with Drinfeld Γ0(p^n)-level structures provides a good integral model and a relative compactification of the moduli space of shtukas with naive Γ0(p^n)-level defined using shtukas for dilated group schemes. For general reductive groups, we embed the moduli space of global shtukas for the deep Bruhat-Tits group scheme into the limit of the moduli spaces of shtukas for all associated parahoric group schemes. We define the integral model of the moduli space of shtukas with deep Bruhat-Tits level as the schematic image of this map and show that the integral models defined in this way admit proper, surjective and generically étale 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