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 -Shtukas with pairwise colliding legs admit -adic uniformization isomorphisms by Rapoport-Zink spaces. Here 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