The regularity of difference divisors

For a prime number \(p>2\) $p>2$ and a finite extension \(F/\mathbb {Q}_p\) $F/{\mathbb{Q}}_p$ , we explain the construction of the difference divisors on the unitary Rapoport–Zink spaces of hyperspecial level over \(\mathcal {O}_{\breve{F}}\) ${\mathcal{O}}_{\breve{F}}$ , and the GSpin Rapoport–Zink spaces of hyperspecial level over \(\breve{\mathbb {Z}}_{p}\) ${\breve{\mathbb{Z}}}_p$ associated to a minuscule cocharacter \(\mu \) $\mu$ 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.