Basic loci in Shimura varieties of Coxeter type

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.

27 pages

References in corpus (1)

• A guide to the reduction modulo p of Shimura varieties

Cited by in corpus (11)

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• Rapoport-Zink spaces for spinor groups
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• On Tate conjecture for the special fibers of some unitary Shimura varieties
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties
• Hecke algebras and $p$-adic groups
• Affine Deligne-Lusztig varieties at infinite level
• Affine Deligne-Lusztig varieties and the action of J
• Stratifications of affine Deligne-Lusztig varieties
• Good and semi-stable reductions of Shimura varieties
• Regular formal moduli spaces and arithmetic transfer conjectures