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Propriétés du groupe tannakien des structures de Hodge p -adiques et torseur entre cohomologies cristalline et étale

Jean-Pierre Wintenberger (1997)

Annales de l'institut Fourier

On donne des propriétés de la catégorie tannakienne des modules de Dieudonné filtrés sur un corps p -adique (ces modules de Dieudonné jouent en p -adique un rôle analogue aux structures de Hodge complexes). On prouve l’existence d’un foncteur fibre sur Q p et la simple connexité du groupe associé. Ceci permet de montrer, sous la conjecture de Fontaine : “faiblement admissible entraîne admissible”, une conjecture de Rapoport et Zink décrivant le torseur entre cohomologie cristalline et étale, et de prouver...

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