Cohen-Macaulayness of Local Models via Shellability of the Admissible Set
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866914374629720064 |
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| author | He, Xuhua Schremmer, Felix Yu, Qingchao |
| author_facet | He, Xuhua Schremmer, Felix Yu, Qingchao |
| contents | We prove that for any dominant cocharacter $μ$ and any parahoric level $K$, the augmented admissible set $\widehat{\Adm(μ)^K}$ in the Iwahori-Weyl group is dual EL-shellable. This resolves a conjecture of Görtz and provides a new proof of the Cohen-Macaulay property for the special fibres of local models with parahoric level structure. In particular, the result settles the previously open cases of residue characteristic $2$ and non-reduced root systems.
This approach is characteristic-free and intrinsic to the structure of admissible sets. Moreover, our construction yields an explicit shelling, which translates into an inductive, component-by-component building procedure for the special fibre that preserves Cohen-Macaulayness at each step.
As a consequence, we obtain the Cohen-Macaulayness of many local models of Shimura varieties considered in the literature, most notably those satisfying the He-Pappas-Rapoport description, as well as the local models characterized by Scholze-Weinstein and constructed by Anschütz-Gleason-Lourenço-Richarz. Via the usual local model diagram, these results imply the Cohen-Macaulay property for the corresponding integral models of Shimura varieties whenever available. This gives a new proof that the integral models constructed by Kisin-Pappas-Zhou are Cohen-Macaulay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulayness of Local Models via Shellability of the Admissible Set He, Xuhua Schremmer, Felix Yu, Qingchao Number Theory Algebraic Geometry Representation Theory 11G25, 20G25 We prove that for any dominant cocharacter $μ$ and any parahoric level $K$, the augmented admissible set $\widehat{\Adm(μ)^K}$ in the Iwahori-Weyl group is dual EL-shellable. This resolves a conjecture of Görtz and provides a new proof of the Cohen-Macaulay property for the special fibres of local models with parahoric level structure. In particular, the result settles the previously open cases of residue characteristic $2$ and non-reduced root systems. This approach is characteristic-free and intrinsic to the structure of admissible sets. Moreover, our construction yields an explicit shelling, which translates into an inductive, component-by-component building procedure for the special fibre that preserves Cohen-Macaulayness at each step. As a consequence, we obtain the Cohen-Macaulayness of many local models of Shimura varieties considered in the literature, most notably those satisfying the He-Pappas-Rapoport description, as well as the local models characterized by Scholze-Weinstein and constructed by Anschütz-Gleason-Lourenço-Richarz. Via the usual local model diagram, these results imply the Cohen-Macaulay property for the corresponding integral models of Shimura varieties whenever available. This gives a new proof that the integral models constructed by Kisin-Pappas-Zhou are Cohen-Macaulay. |
| title | Cohen-Macaulayness of Local Models via Shellability of the Admissible Set |
| topic | Number Theory Algebraic Geometry Representation Theory 11G25, 20G25 |
| url | https://arxiv.org/abs/2603.05875 |