English

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

Number Theory 2023-10-02 v1 Algebraic Geometry

Abstract

We show that the moduli spaces of bounded global G\mathcal{G}-Shtukas with pairwise colliding legs admit pp-adic uniformization isomorphisms by Rapoport-Zink spaces. Here G\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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Cite

@article{arxiv.2309.17441,
  title  = {Uniformizing the moduli stacks of global $G$-Shtukas II},
  author = {Urs Hartl and Yujie Xu},
  journal= {arXiv preprint arXiv:2309.17441},
  year   = {2023}
}

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53 pages