Affine Deligne-Lusztig varieties in affine flag varieties

Abstract

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.

44 pages, 4 figures. Minor changes to font, references, and acknowledgments. Improved introduction, other improvements in exposition, and two new figures added, for a total of 4

Cited by in corpus (9)

• The Newton stratification on deformations of local G-shtukas
• Foliations in deformation spaces of local G-shtukas
• On the connected components of affine Deligne-Lusztig varieties
• The geometry of Newton strata in the reduction modulo $p$ of Shimura varieties of PEL type
• Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
• Chimney retractions in affine buildings encode orbits in affine flag varieties
• Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits
• Newton Strata in Levi Subgroups
• $p$-kernels occurring in an isogeny class of $p$-divisible groups