Basic loci of Coxeter type with arbitrary parahoric level
Algebraic Geometry
2020-09-21 v2 Number Theory
Abstract
Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their "group-theoretic models" -- generalized affine Deligne-Lusztig varieties -- in cases where they have a particularly nice description. Continuing the work of [GH] and [GHN] we single out the class of cases of Coxeter type, give a characterization in terms of the dimension, and obtain a complete classification. We also discuss known, new and open cases from the point of view of Shimura varieties/Rapoport-Zink spaces.
Cite
@article{arxiv.2006.08838,
title = {Basic loci of Coxeter type with arbitrary parahoric level},
author = {Ulrich Görtz and Xuhua He and Sian Nie},
journal= {arXiv preprint arXiv:2006.08838},
year = {2020}
}
Comments
33 pages. A new section on the smoothness of closures of strata is added