Regular integral models for Shimura varieties of orthogonal type

TL;DR

This paper constructs regular p-adic integral models for Shimura varieties of orthogonal type, using explicit local models and combining recent theoretical results, to better understand their arithmetic properties over odd primes.

Contribution

It provides explicit regular integral models for orthogonal Shimura varieties at certain primes, advancing the understanding of their arithmetic and geometric structure.

Findings

Constructed regular p-adic integral models over odd primes

Resolved local models explicitly for these varieties

Connected the models with existing theoretical frameworks

Abstract

We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular p-adic integral models for these varieties over odd primes p at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.