Irreducibility of Local Models

TL;DR

This paper studies the geometric irreducibility of local models associated with Shimura varieties and G-Shtukas, classifying when they are irreducible and analyzing fibers of level-changing maps.

Contribution

It provides a classification of irreducible local models and demonstrates that fibers of level-changing maps are always irreducible Schubert varieties.

Findings

Classification of irreducible local models

Fibers of level-changing maps are irreducible Schubert varieties

Enhanced understanding of geometric structures in Shimura varieties

Abstract

In this paper, we consider the geometric special fibers of local models of Shimura varieties and of moduli of $\bG$-Shtukas with parahoric level structure. We investigate two problems with respect to the irreducibility of local models. First, we classify the cases where the local models are irreducible. Next, we show that the fibers of the level-changing map between the geometric special fiber of local models with different parahoric levels are always isomorphic to single (i.e., irreducible) Schubert varieties in the partial flag variety.