Irreducibility of the Hilbert-Blumenthal moduli spaces with parahoric level structure

TL;DR

This paper calculates the number of irreducible components in the reduction modulo p of Hilbert-Blumenthal moduli spaces with parahoric level structure, focusing on cases where p is unramified in the totally real field.

Contribution

It provides a precise count of irreducible components for these moduli spaces, extending understanding of their geometric structure in the unramified case.

Findings

Number of irreducible components determined

Results apply to unramified primes in totally real fields

Advances the understanding of moduli space geometry

Abstract

We determine the number of irreducible components of the reduction mod p of any Hilbert-Blumenthal moduli space with a parahoric level structure, where p is unramified in the totally real field.