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Groupes analytiques rigides p-divisibles II

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Abstract

Let K be a p-adic field. We continue to develop the theory of rigid analytic p-divisible groups over K. For example, we explain how to recover the category of Banach–Colmez spaces from rigid analytic p-divisible groups “at finite level” without perfectoid spaces. We then establish some results about families of rigid analytic p-divisible groups. This allows us to prove a “minimality” result in the sense of birational geometry for integral models of unramified Rapoport–Zink spaces.

Résumé

Soit K un corps p-adique. On continue de développer la théorie des groupes analytiques rigides p-divisibles sur K. On explique par exemple comment retrouver la catégorie des espaces de Banach–Colmez à partir des groupes analytiques rigides p-divisibles \(\ll \) en niveau fini\(\gg \) sans espaces perfectoïdes. On établit ensuite des résultats sur les familles de groupes analytiques rigides p-divisibles. Cela nous permet de démontrer un théorème de \(\ll \) minimalité\(\gg \) au sens de la géométrie birationnelle des modèles entiers des espaces de Rapoport–Zink non-ramifiés.

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  • 21 September 2022

    “ORCID number of author Laurent Fargues updated”.

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  1. CNRS, Institut de Mathématiques de Jussieu, 4 place Jussieu, Paris, 75252, France

    Laurent Fargues

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  1. Laurent Fargues
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Fargues, L. Groupes analytiques rigides p-divisibles II. Math. Ann. 387, 245–264 (2023). https://doi.org/10.1007/s00208-022-02453-1

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