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arXiv · 1311.6263

Basic loci in Shimura varieties of Coxeter type

Ulrich Goertz·Xuhua He
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Abstract

This paper is a contribution to the general problem of giving an explicit description of the basic locus in the reduction modulo $p$ of Shimura varieties. Motivated by \cite{Vollaard-Wedhorn} and \cite{Rapoport-Terstiege-Wilson}, we classify the cases where the basic locus is (in a natural way) the union of classical Deligne-Lusztig sets associated to Coxeter elements. We show that if this is satisfied, then the Newton strata and Ekedahl-Oort strata have many nice properties.

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Ulrich Goertz, Xuhua He. 2013-11-25. Basic loci in Shimura varieties of Coxeter type. https://arxiv.org/abs/1311.6263

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