Invariants de Hasse $\mu$-ordinaires

Hernandez, Valentin

Annales de l'Institut Fourier, Tome 68 (2018) no. 4, pp. 1519-1607.

Dans cet article on se propose de construire d’une manière purement locale des invariants partiels pour des groupes $p$-divisibles munis d’endomorphismes, en utilisant des résultats de cohomologie cristalline. Ces invariants généralisent l’invariant de Hasse, et permettent d’étudier des familles de tels groupes. On étudie aussi différentes propriétés géométriques de ces invariants. Appliqués (par exemple) à certaines variétés de Shimura, ces invariants détectent certaines strates de Newton, notamment la strate $\mu$-ordinaire.

In this article, we construct in a purely local way partial (Hasse) invariants for $p$-divisible groups with given endomorphisms, using crystalline cohomology. These invariants generalises the classical Hasse invariant, and allow us to study families of such groups. We also study a few geometric properties of these invariants. Used in the context of Shimura varieties, for example, these invariants are detecting some Newton strata, including the $\mu$-ordinary locus.

Classification : 14L05, 11G25 11G18, 11G07, 11G15
Mot clés : Groupes $p$-divisibles, cristaux et isocristaux, Variétés de Shimura, lieu $\mu$-ordinaire, Stratification de Newton, invariants de Hasse, multiplication complexe et espaces de modules de groupes $p$-divisibles.
Keywords: $p$-divisible groups, cristals and isocristals, Shimura Varieties, $\mu$-ordinary locus, Newton stratification, Hasse invariants, Complex multiplication and moduli space of $p$-divisible groups.

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