Uniformizing the moduli stacks of global $G$-Shtukas II

TL;DR

This paper establishes p-adic uniformization for moduli spaces of global G-Shtukas with colliding legs, extending previous results to more general group schemes, and proves the Langlands-Rapoport Conjecture in this setting.

Contribution

It generalizes uniformization results to non-parahoric group schemes and applies this to prove the Langlands-Rapoport Conjecture over function fields.

Findings

Uniformization isomorphisms by Rapoport-Zink spaces for broader class of G-Shtukas.

Proof of the Langlands-Rapoport Conjecture over function fields with colliding legs.

Extension of uniformization techniques beyond hyperspecial and parahoric cases.

Abstract

We show that the moduli spaces of bounded global $\mathcal{G}$-Shtukas with pairwise colliding legs admit $p$-adic uniformization isomorphisms by Rapoport-Zink spaces. Here $\mathcal{G}$ is a smooth affine group scheme with connected fibers and reductive generic fiber, i.e. we do not assume it to be parahoric, or even hyperspecial. Moreover, we deduce the Langlands-Rapoport Conjecture over function fields in the case of colliding legs using our uniformization theorem.