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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.16092 |
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| _version_ | 1866909047237640192 |
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| author | Vanhaecke, Arnaud |
| author_facet | Vanhaecke, Arnaud |
| contents | In the seventies, V. G. Drinfeld proved that a moduli problem of deformations by quasi-isogenies of certain $p$-divisible groups with extra actions is representable by an explicit semi-stable model of the $p$-adic symmetric space. This theorem, known as \emph{Drinfeld's representability theorem}, has been one of the cornerstones of geometric aspects in $p$-adic Hodge theory. The purpose of these notes is twofold. On the one hand we give a new and more transparent proof of Drinfeld's representability theorem; on the other hand, we give a detailed presentation of Drinfeld's moduli space and the formal model of the $p$-adic symmetric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Drinfeld's representability theorem Vanhaecke, Arnaud Number Theory Algebraic Geometry 11S31, 14L05, 14GXX, 20E42 In the seventies, V. G. Drinfeld proved that a moduli problem of deformations by quasi-isogenies of certain $p$-divisible groups with extra actions is representable by an explicit semi-stable model of the $p$-adic symmetric space. This theorem, known as \emph{Drinfeld's representability theorem}, has been one of the cornerstones of geometric aspects in $p$-adic Hodge theory. The purpose of these notes is twofold. On the one hand we give a new and more transparent proof of Drinfeld's representability theorem; on the other hand, we give a detailed presentation of Drinfeld's moduli space and the formal model of the $p$-adic symmetric space. |
| title | On Drinfeld's representability theorem |
| topic | Number Theory Algebraic Geometry 11S31, 14L05, 14GXX, 20E42 |
| url | https://arxiv.org/abs/2605.16092 |