A relation between zip stacks and moduli stacks of truncated local shtukas
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929741755318272 |
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| author | Yan, Qijun |
| author_facet | Yan, Qijun |
| contents | Let \(G\) be a reductive group over a field \(k\), and let \(μ\) be a cocharacter of \(G\). We prove that Viehmann's double coset spaces associated with \((G, μ)\) are representable by certain Lusztig varieties, and establish a similar result for the mixed characteristic case. This representability enables a comparison between the moduli stacks of truncated local shtukas and zip stacks. Over a perfect field of positive characteristic, we establish a homeomorphism between the coarse moduli stack of \(1\text{-}1\)-truncated local \(G\)-shtukas and that of \(G\)-zips, thereby enriching our understanding of zip period maps in the context of Shimura varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12204 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A relation between zip stacks and moduli stacks of truncated local shtukas Yan, Qijun Algebraic Geometry Number Theory Representation Theory 14G17 14G35 Let \(G\) be a reductive group over a field \(k\), and let \(μ\) be a cocharacter of \(G\). We prove that Viehmann's double coset spaces associated with \((G, μ)\) are representable by certain Lusztig varieties, and establish a similar result for the mixed characteristic case. This representability enables a comparison between the moduli stacks of truncated local shtukas and zip stacks. Over a perfect field of positive characteristic, we establish a homeomorphism between the coarse moduli stack of \(1\text{-}1\)-truncated local \(G\)-shtukas and that of \(G\)-zips, thereby enriching our understanding of zip period maps in the context of Shimura varieties. |
| title | A relation between zip stacks and moduli stacks of truncated local shtukas |
| topic | Algebraic Geometry Number Theory Representation Theory 14G17 14G35 |
| url | https://arxiv.org/abs/2308.12204 |