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arXiv · 2006.07271

On orthogonal local models of Hodge type

Ioannis Zachos
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Abstract

We study local models that describe the singularities of Shimura varieties of non-PEL type for orthogonal groups at primes where the level subgroup is given by the stabilizer of a single lattice. In particular, we use the Pappas-Zhu construction and we give explicit equations that describe an open subset around the "worst" point of orthogonal local models given by a single lattice. These equations display the affine chart of the local model as a hypersurface in a determinantal scheme. Using this we prove that the special fiber of the local model is reduced and Cohen-Macaulay.

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Ioannis Zachos. 2020-06-12. On orthogonal local models of Hodge type. https://arxiv.org/abs/2006.07271

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