Topological flatness of orthogonal spin local models

TL;DR

This paper proves that certain spin local models associated with orthogonal similitude groups over discretely valued fields are topologically flat, advancing the understanding of their geometric properties in algebraic geometry.

Contribution

It establishes the topological flatness of spin local models for split even orthogonal similitude groups, confirming a preliminary form of the Pappas-Rapoport flatness conjecture.

Findings

Proves topological flatness of spin local models

Advances understanding of local models in algebraic geometry

Supports the Pappas-Rapoport flatness conjecture

Abstract

Let $p$ be an odd prime and $F$ be a complete discretely valued field with residue field of characteristic $p$. For any parahoric level structure of the split even orthogonal similitude group $\operatorname{GO}_{2n}$ over $F$, we prove a preliminary form of the Pappas-Rapoport flatness conjecture: the associated spin local model is topologically flat.