PEL moduli spaces without $\mathbb C$-valued points

TL;DR

This paper explores new ways to interpret fibers of Shimura varieties over various primes, showing that bounded symmetric domains can have quotients with good reduction at primes dividing those domains.

Contribution

It provides novel moduli interpretations of Shimura variety fibers and demonstrates the existence of quotients with good reduction at specific primes.

Findings

New moduli interpretations of Shimura variety fibers

Existence of quotients with good reduction at primes dividing the domain

Applications to bounded symmetric domains and arithmetic groups

Abstract

We give several new moduli interpretations of the fibers of certain Shimura varieties over several prime numbers. As a consequence (of our theorem 9.1) one obtains that for every prescribed odd prime characteristic $p$ every bounded symmetric domain possesses quotients by arithmetic groups whose models have good reduction at a prime divisor of $p$.