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La filtration canonique des \({{\mathcal {O}}}\)-modules p-divisibles

  • Valentin HernandezEmail author
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Abstract

In this article we associate to G, a truncated p-divisible \({{\mathcal {O}}}\)-module of given signature, where \({{\mathcal {O}}}\) is a finite unramified extension of \(\mathbb {Z}_p\), a filtration of G by sub-\({{\mathcal {O}}}\)-modules under the condition that its Hasse \(\mu \)-invariant is smaller than an explicit bound. This filtration generalise the one given when G is \(\mu \)-ordinary. The construction of the filtration relies on a precise study of the crystalline periods of a p-divisible \({{\mathcal {O}}}\)-module. We then apply this result to families of such groups, in particular to strict neighbourhoods of the \(\mu \)-ordinary locus inside some PEL Shimura varieties.

Résumé

Dans cet article, à G un groupe p-divisible tronqué muni d’une action d’une extension finie non ramifiée \({{\mathcal {O}}}\) de \(\mathbb {Z}_p\), et de signature donnée, on associe sous une condition explicite sur son \(\mu \)-invariant de Hasse, une filtration de G par des sous-\({{\mathcal {O}}}\)-modules qui étend la filtration canonique lorsque G est \(\mu \)-ordinaire. La construction se fait en étudiant les périodes cristallines des groupes p-divisibles avec action de \({{\mathcal {O}}}\). On applique ensuite cela aux familles de tels groupes, en particulier des voisinages stricts du lieu \(\mu \)-ordinaire dans des variétés de Shimura PEL.

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université Paris-SudOrsayFrance

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