Normality and Cohen-Macaulayness of parahoric local models
Abstract
We study the singularities of integral models of Shimura varieties and moduli stacks of shtukas with parahoric level structure. More generally our results apply to the Pappas-Zhu and Levin mixed characteristic parahoric local models, and to their equal characteristic analogues. For any such local model we prove under minimal assumptions that the entire local model is normal with reduced special fiber and, if , it is also Cohen-Macaulay. This proves a conjecture of Pappas and Zhu, and shows that the integral models of Shimura varieties constructed by Kisin and Pappas are Cohen-Macaulay as well.
Keywords
Cite
@article{arxiv.1903.10585,
title = {Normality and Cohen-Macaulayness of parahoric local models},
author = {Thomas J. Haines and Timo Richarz},
journal= {arXiv preprint arXiv:1903.10585},
year = {2019}
}
Comments
The statements have been changed to reflect the fact that in bad characteristic Schubert varieties can fail to be normal. We have removed the assertion that all Schubert varieties in bad characteristic are normal. The Cohen-Macaulayness of local models is now proved under a minimal assumption