# On the $\mu$-ordinary locus of a Shimura variety

## TL;DR

This paper investigates the structure and density criteria of the $$-ordinary locus within Shimura varieties with parahoric level, linking it to Ekedahl-Kottwitz-Oort-Rapoport strata.

## Contribution

It establishes that the $$-ordinary locus is a union of specific strata and provides criteria for its density under certain axioms.

## Key findings

- The $$-ordinary locus is a union of maximal Ekedahl-Kottwitz-Oort-Rapoport strata.
- Criteria for the density of the $$-ordinary locus are provided.
- The results are valid under the axioms outlined in .

## Abstract

In this paper, we study the $\mu$-ordinary locus of a Shimura variety with parahoric level structure. Under the axioms in \cite{HR}, we show that $\mu$-ordinary locus is a union of some maximal Ekedahl-Kottwitz-Oort-Rapoport strata introduced in \cite{HR} and we give criteria on the density of the $\mu$-ordinary locus.