On the Bruhat-Tits stratification of a quaternionic unitary Shimura variety

Abstract

In this note we study the special fiber of the Rapoport-Zink space attached to a quaternionic unitary group. The special fiber is described using the so called Bruhat-Tits stratification and is intimately related to the Bruhat-Tits building of a split symplectic group. As an application we describe the supersingular locus of the related Shimura variety.

revised

References in corpus (6)

• Rapoport-Zink spaces for spinor groups
• Fully Hodge-Newton decomposable Shimura varieties
• The supersingular locus of unitary Shimura varieties with exotic good reduction
• On Tate conjecture for the special fibers of some unitary Shimura varieties
• A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds
• Stratifications of affine Deligne-Lusztig varieties

Cited by in corpus (2)

• On quaternionic unitary Rapoport-Zink spaces with parahoric level structures
• On the supersingular locus of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified prime