On properness of moduli stacks of $D^{\times}$-shtukas over ramified legs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910967445585920 |
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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 |