Stratifications of affine Deligne-Lusztig varieties

2018/02/06 by Ulrich Goertz, Goertz, Ulrich
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1802.02225

Abstract

Affine Deligne-Lusztig varieties are analogues of Deligne-Lusztig varieties in the context of affine flag varieties and affine Grassmannians. They are closely related to moduli spaces of p-divisible groups in positive characteristic, and thus to arithmetic properties of Shimura varieties. We compare stratifications of affine Deligne-Lusztig varieties attached to a basic element b. In particular, we show that the stratification defined by Chen and Viehmann using the relative position to elements of the group J_b, the σ-centralizer of b, coincides with the Bruhat-Tits stratification in all cases of Coxeter type, as defined by X. He and the author.

Citations

• A guide to the reduction modulo p of Shimura varieties

Related

• Affine Deligne-Lusztig varieties and the action of J
• The Ekedahl-Oort Stratification and the Semi-Module Stratification
• Affine Deligne-Lusztig Varieties of Positive Coxeter Type
• Irreducible components of affine Deligne-Lusztig varieties
• Lifting Deligne-Lusztig Reduction and Geometric Coxeter Type Elements