On the Bruhat-Tits stratification of a quaternionic unitary Shimura variety
Haining Wang
TL;DR
This paper investigates the structure of the special fiber of a Rapoport-Zink space linked to a quaternionic unitary group, using Bruhat-Tits stratification, and describes the supersingular locus of the associated Shimura variety.
Contribution
It provides a detailed description of the Bruhat-Tits stratification of the special fiber and its relation to the Bruhat-Tits building, advancing understanding of quaternionic unitary Shimura varieties.
Findings
Description of the Bruhat-Tits stratification of the special fiber
Relation between the stratification and the Bruhat-Tits building
Characterization of the supersingular locus
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models