Basic loci of Coxeter type in Shimura varieties

Ulrich Gortz University of Duisburg-Essen Xuhua He University of Maryland

Arithmetic Geometry and Commutative Algebra mathscidoc:1803.07005

Distinguished Paper Award in 2018

Camb. J. Math., 3, 323-353, 2015
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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  title={Basic loci of Coxeter type in Shimura varieties},
  author={Ulrich Gortz, and Xuhua He},
  booktitle={Camb. J. Math.},
Ulrich Gortz, and Xuhua He. Basic loci of Coxeter type in Shimura varieties. 2015. Vol. 3. In Camb. J. Math.. pp.323-353.
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