On properness of moduli stacks of $D^{\times}$-shtukas over ramified legs

Fuente: arXiv
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Autores principales: Choi, Yong-Gyu, Kim, Wansu, Park, Junyeong
Formato: Preprint
Publicado: 2025
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author Choi, Yong-Gyu
Kim, Wansu
Park, Junyeong
author_facet Choi, Yong-Gyu
Kim, Wansu
Park, Junyeong
contents Given a maximal order $D$ of a central division algebra over a global function field $F$, we prove an explicit sufficient condition for moduli stacks of $D^\times$-shtukas to be proper over a finite field in terms of the local invariants of $D$ and bounds. Our proof is a refinement of E.~Lau's result (Duke Math. J. 140 (2007)), which showed the properness of the leg morphism (or characteristic morphism) away from the ramification locus of $D$. We also establish non-emptiness of Newton and Kottwitz--Rapoport strata for moduli stacks of $B^\times$-shtukas, where $B$ is a maximal order of a central simple algebra over $F$.
format Preprint
id arxiv_https___arxiv_org_abs_2505_18977
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On properness of moduli stacks of $D^{\times}$-shtukas over ramified legs
Choi, Yong-Gyu
Kim, Wansu
Park, Junyeong
Number Theory
Algebraic Geometry
14H60, 14D23, 14G35
Given a maximal order $D$ of a central division algebra over a global function field $F$, we prove an explicit sufficient condition for moduli stacks of $D^\times$-shtukas to be proper over a finite field in terms of the local invariants of $D$ and bounds. Our proof is a refinement of E.~Lau's result (Duke Math. J. 140 (2007)), which showed the properness of the leg morphism (or characteristic morphism) away from the ramification locus of $D$. We also establish non-emptiness of Newton and Kottwitz--Rapoport strata for moduli stacks of $B^\times$-shtukas, where $B$ is a maximal order of a central simple algebra over $F$.
title On properness of moduli stacks of $D^{\times}$-shtukas over ramified legs
topic Number Theory
Algebraic Geometry
14H60, 14D23, 14G35
url https://arxiv.org/abs/2505.18977