Dans cet article on se propose de construire d’une manière purement locale des invariants partiels pour des groupes -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 -ordinaire.
In this article, we construct in a purely local way partial (Hasse) invariants for -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 -ordinary locus.
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Mots-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.
Hernandez, Valentin 1
CC-BY-ND 4.0
@article{AIF_2018__68_4_1519_0,
author = {Hernandez, Valentin},
title = {Invariants de {Hasse} $\mu $-ordinaires},
journal = {Annales de l'Institut Fourier},
pages = {1519--1607},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {68},
number = {4},
year = {2018},
doi = {10.5802/aif.3193},
language = {fr},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3193/}
}
TY - JOUR AU - Hernandez, Valentin TI - Invariants de Hasse $\mu $-ordinaires JO - Annales de l'Institut Fourier PY - 2018 SP - 1519 EP - 1607 VL - 68 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3193/ DO - 10.5802/aif.3193 LA - fr ID - AIF_2018__68_4_1519_0 ER -
%0 Journal Article %A Hernandez, Valentin %T Invariants de Hasse $\mu $-ordinaires %J Annales de l'Institut Fourier %D 2018 %P 1519-1607 %V 68 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3193/ %R 10.5802/aif.3193 %G fr %F AIF_2018__68_4_1519_0
Hernandez, Valentin. Invariants de Hasse $\mu $-ordinaires. Annales de l'Institut Fourier, Tome 68 (2018) no. 4, pp. 1519-1607. doi : 10.5802/aif.3193. https://aif.centre-mersenne.org/articles/10.5802/aif.3193/
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