Truncations of level 1 of elements in the loop group of a reductive group

Abstract

We generalize the notion of Ekedahl-Oort strata to elements in the loop group of any connected reductive group, and call the resulting discrete invariant the truncation of level 1 of the element. We give conditions for the Newton points occurring among the elements of a given truncation of level 1 and especially for the generic Newton point in a given truncation stratum. We prove that truncation strata are locally closed and give a description of the closure of each stratum. We also translate our results back to the original Ekedahl-Oort stratification of the reduction modulo p of Shimura varieties.

22 pages, final version

References in corpus (2)

• Foliations in deformation spaces of local G-shtukas
• The supersingular locus in Siegel modular varieties with Iwahori level structure

Cited by in corpus (5)

• Ekedahl-Oort and Newton strata for Shimura varieties of PEL type
• Minimal length elements in conjugacy classes of extended affine Weyl group
• Basic loci in Shimura varieties of Coxeter type
• Foliations in deformation spaces of local G-shtukas
• On some partitions of an affine flag variety