The \mu-ordinary Hasse invariant of unitary Shimura varieties

TL;DR

This paper generalizes the Hasse invariant for PEL type A Shimura varieties, providing a tool to identify the -ordinary locus in good reduction cases, enhancing understanding of their geometric structure.

Contribution

It introduces a new -ordinary Hasse invariant applicable to all PEL type A Shimura varieties over primes of good reduction.

Findings

Constructed a -ordinary Hasse invariant for these varieties.

The invariant's vanishing locus coincides with the -ordinary locus.

Provides a geometric characterization of the -ordinary locus.

Abstract

We construct a generalization of the Hasse invariant for any Shimura variety of PEL type A over a prime of good reduction, whose vanishing locus is the open and dense \mu-ordinary locus.