The regularity of difference divisors

TL;DR

This paper studies the structure of difference divisors on certain Rapoport-Zink spaces, proving their regularity and identifying smooth loci using deformation theory, advancing understanding in arithmetic geometry.

Contribution

It provides a new deformation-theoretic proof of the regularity of difference divisors on unitary and GSpin Rapoport-Zink spaces, and describes their smooth loci.

Findings

Proves the regularity of difference divisors on specified Rapoport-Zink spaces.

Identifies the formally smooth locus of special cycles and difference divisors.

Uses a purely deformation-theoretic approach for the proofs.

Abstract

For a prime number $p>2$, we explain the construction of the difference divisors on the unitary Rapoport-Zink spaces of hyperspecial level and the GSpin Rapoport-Zink spaces of hyperspecial level associated to a minuscule cocharacter $\mu$ and a basic element $b$. We prove the regularity of the difference divisors, find the formally smooth locus of both the special cycles and the difference divisors, by a purely deformation-theoretic approach.