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arXiv · 2309.17441

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

Urs Hartl·Yujie Xu
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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.

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Urs Hartl, Yujie Xu. 2023-09-29. Uniformizing the moduli stacks of global $G$-Shtukas II. https://arxiv.org/abs/2309.17441

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