Cohen-Macaulayness of Local Models via Shellability of the Admissible Set

Uploaded April 2026 | Updated September 2026, 3 weeks ago

Joint IAS/PU Arithmetic Geometry

Topic: Cohen-Macaulayness of Local Models via Shellability of the Admissible Set
Speaker: Xuhua He
Affiliation: Chinese University of Hong Kong
Date: April 20, 2026
Simonyi 101

The singularities of integral models of Shimura varieties are encoded in their local models, schemes over the
p
-adic integers whose special fibers are unions of affine Schubert cells. A fundamental question is whether these local models are Cohen-Macaulay.In this talk, I will present a solution for local models with arbitrary parahoric level structure, valid uniformly across all residue characteristics. The proof is centered on a combinatorial property of the admissible set, which parametrizes the cells in the special fiber. We prove that the admissible set is dual EL-shellable, thereby resolving a conjecture of Görtz from over two decades ago. From this purely combinatorial result, we deduce the Cohen-Macaulay property for the corresponding local models.This work provides a uniform, characteristic-independent approach that contrasts with and complements prior geometric methods. I will explain the key combinatorial ideas and their translation into this geometric consequence.

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