On the geometry of the Pappas-Rapoport models for PEL Shimura varieties

TL;DR

This paper investigates the geometric properties of Pappas-Rapoport models for ramified PEL Shimura varieties, demonstrating smoothness in most cases and analyzing their special fibers and stratifications.

Contribution

It provides new insights into the smoothness and stratification structures of Pappas-Rapoport models in ramified settings, extending previous unramified results.

Findings

Models are smooth outside a specific ramified case.

The special fiber exhibits interesting stratifications.

The $mbda$-ordinary locus is open and dense.

Abstract

We study integral models, so-called Pappas-Rapoport or splitting models, of some PEL Shimura Varieties whose data are ramified at a prime p. We show that except in a specific case, these models are smooth when there is no level at p, and we study their special fiber modulo p. We show that interesting stratifications appear, and we show that the $\mu$-ordinary locus is open and dense, following a strategy of Wedhorn in the unramified case.