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arXiv · 2505.18977

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

Yong-Gyu Choi·Wansu Kim·Junyeong Park
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Abstract

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 $F$.

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Yong-Gyu Choi, Wansu Kim, Junyeong Park. 2025-05-25. On properness of moduli stacks of $D^{\times}$-shtukas over ramified legs. https://arxiv.org/abs/2505.18977

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