Stratifications of affine Deligne-Lusztig varieties

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 $\sigma$-centralizer of $b$, coincides with the Bruhat-Tits stratification in all cases of Coxeter type, as defined by X. He and the author.

References in corpus (2)

• A guide to the reduction modulo p of Shimura varieties
• The supersingular locus of unitary Shimura varieties with exotic good reduction

Cited by in corpus (3)

• On the Bruhat-Tits stratification of a quaternionic unitary Shimura variety
• On quaternionic unitary Rapoport-Zink spaces with parahoric level structures
• On the Bruhat-Tits stratification for GU(2,2) type Rapoport-Zink space: unramified case