2023/09/20 by Stefania Trentin, Trentin, Stefania
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2309.11290
openalex publication_date 2023/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study the supersingular locus of the Shimura variety associated to the unitary group GU(2,4) over a ramified prime. We show that the associated Rapoport-Zink space is flat, and we give an explicit description of the irreducible components of the reduction modulo p of the basic locus. In particular, we show that these are universally homeomorphic to either a generalized Deligne-Lusztig variety for a symplectic group or to the closure of a vector bundle over a classical Deligne-Lusztig variety for an orthogonal group. Our results are confirmed in the group-theoretical setting by the reduction method à la Deligne and Lusztig and the study of the admissible set.