Logarithmic Dieudonné theory and overconvergent extensions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917166005092352 |
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| author | D'Addezio, Marco |
| author_facet | D'Addezio, Marco |
| contents | In the proof of Crew's parabolicity conjecture, we established a key property concerning the slopes of $\dagger$-hulls of $F$-isocrystals, extending a result of Tsuzuki. This article presents an alternative proof of this theorem for a specific class of $F$-isocrystals. The central ingredient is a local extension property for étale $p$-divisible subgroups. To relate $p$-divisible groups and overconvergent $F$-isocrystals, we employ logarithmic Dieudonné theory, as introduced by Kato and further developed by Inoue. Over curves, this leads to an equivalence between the category of potentially semi-stable $p$-divisible groups and overconvergent $F$-isocrystals with slopes in the interval $[0,1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic Dieudonné theory and overconvergent extensions D'Addezio, Marco Algebraic Geometry Number Theory 14A21, 14F30, 14G17, 14L05 In the proof of Crew's parabolicity conjecture, we established a key property concerning the slopes of $\dagger$-hulls of $F$-isocrystals, extending a result of Tsuzuki. This article presents an alternative proof of this theorem for a specific class of $F$-isocrystals. The central ingredient is a local extension property for étale $p$-divisible subgroups. To relate $p$-divisible groups and overconvergent $F$-isocrystals, we employ logarithmic Dieudonné theory, as introduced by Kato and further developed by Inoue. Over curves, this leads to an equivalence between the category of potentially semi-stable $p$-divisible groups and overconvergent $F$-isocrystals with slopes in the interval $[0,1]$. |
| title | Logarithmic Dieudonné theory and overconvergent extensions |
| topic | Algebraic Geometry Number Theory 14A21, 14F30, 14G17, 14L05 |
| url | https://arxiv.org/abs/2512.20143 |