A Dieudonné theory for analytic p-divisible groups and applications to Shimura varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915778053275648 |
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| author | Gerth, Lucas |
| author_facet | Gerth, Lucas |
| contents | We study families of analytic $p$-divisible groups over adic spaces $S$ defined over $\mathbb{Q}_p$. We prove an equivalence between such families and Hodge-Tate triples, generalizing a theorem of Fargues. For a perfectoid space $S$, we construct a functor associating to an analytic $p$-divisible group $\mathcal{G} \rightarrow S$ a coherent sheaf $\mathcal{E}(\mathcal{G})$ on the relative Fargues--Fontaine curve $X_S$. Restricting to analytic $p$-divisible groups admitting a Cartier dual, we obtain an equivalence of categories with local shtukas satisfying a minuscule condition, compatible with the prismatic Dieudonné theory of Anschütz--Le Bras. We conclude with applications to moduli spaces: we show that the local Shimura varieties of EL and PEL types of Scholze--Weinstein are moduli spaces of analytic $p$-divisible groups with extra structure, and we give a reinterpretation of the Hodge--Tate period map of Scholze in terms of topologically $p$-torsion subgroups of abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Dieudonné theory for analytic p-divisible groups and applications to Shimura varieties Gerth, Lucas Algebraic Geometry Number Theory 14G45, 14L05 We study families of analytic $p$-divisible groups over adic spaces $S$ defined over $\mathbb{Q}_p$. We prove an equivalence between such families and Hodge-Tate triples, generalizing a theorem of Fargues. For a perfectoid space $S$, we construct a functor associating to an analytic $p$-divisible group $\mathcal{G} \rightarrow S$ a coherent sheaf $\mathcal{E}(\mathcal{G})$ on the relative Fargues--Fontaine curve $X_S$. Restricting to analytic $p$-divisible groups admitting a Cartier dual, we obtain an equivalence of categories with local shtukas satisfying a minuscule condition, compatible with the prismatic Dieudonné theory of Anschütz--Le Bras. We conclude with applications to moduli spaces: we show that the local Shimura varieties of EL and PEL types of Scholze--Weinstein are moduli spaces of analytic $p$-divisible groups with extra structure, and we give a reinterpretation of the Hodge--Tate period map of Scholze in terms of topologically $p$-torsion subgroups of abelian varieties. |
| title | A Dieudonné theory for analytic p-divisible groups and applications to Shimura varieties |
| topic | Algebraic Geometry Number Theory 14G45, 14L05 |
| url | https://arxiv.org/abs/2602.05764 |