The supersingular locus of unitary Shimura varieties with exotic good reduction

Abstract

In this paper, we use a group-theoretic approach to give a concrete description of the geometric structure of the supersingular locus of unitary Shimura varieties with exotic good reduction. This approach also is a more uniform way to prove results of this form obtained previously by, for example, Vollaard-Wedhorn and Rapoport-Terstiege-Wilson.

arXiv comment35 pages, added references

References in corpus (5)

• A guide to the reduction modulo p of Shimura varieties
• Towards a theory of local Shimura varieties
• On parahoric subgroups
• On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
• Affine Deligne-Lusztig varieties and the action of J

Cited by in corpus (6)

• Fully Hodge-Newton decomposable Shimura varieties
• On the Bruhat-Tits stratification of a quaternionic unitary Shimura variety
• Stratifications of affine Deligne-Lusztig varieties
• Regular formal moduli spaces and arithmetic transfer conjectures
• On the supersingular locus of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified prime
• On the Bruhat-Tits stratification for GU(2,2) type Rapoport-Zink space: unramified case