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Analysis of the basic locus in shimura varieties linked to spinor similitudes, suggesting implications for self-dual structures.
We study the basic locus of Shimura varieties associated to the group of spinor similitudes of a quadratic space over Q with level structure given by the stabilizer of a vertex lattice. We give a description of the underlying reduced scheme of the associated Rapoport--Zink space, generalizing results of Howard--Pappas [HP17] and Oki [Oki20b], in the case of self-dual, and almost self dual level structure.
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He et al. (2025) studied this question.
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