Invariants de Hasse $\mu$-ordinaires

TL;DR

This paper introduces local partial Hasse invariants for p-divisible groups with endomorphisms, generalizing the classical invariant and aiding the study of their geometric and stratification properties, especially in Shimura varieties.

Contribution

It constructs new local invariants for p-divisible groups with endomorphisms using crystalline cohomology, extending classical Hasse invariants and analyzing their geometric significance.

Findings

Invariants detect Newton strata in Shimura varieties.

Generalization of classical Hasse invariant to p-divisible groups.

Provides tools for studying μ-ordinary locus.

Abstract

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