On the regularity of special difference divisors

TL;DR

This paper proves that the difference divisors linked to special cycles on certain unitary Rapoport-Zink spaces are always regular, establishing a key geometric property in the unramified case.

Contribution

It demonstrates the regularity of difference divisors for special cycles on unitary Rapoport-Zink spaces in the unramified setting, a previously unproven property.

Findings

Difference divisors are always regular in the unramified case

Supports the geometric understanding of special cycles on Rapoport-Zink spaces

Advances the theory of unitary Shimura varieties

Abstract

In this note we prove that the difference divisors associated with special cycles on unitary Rapoport-Zink spaces of signature (1,n-1) in the unramified case are always regular.