On the Rapoport-Zink space for $\mathrm{GU}(2, 4)$ over a ramified prime
Number Theory
2023-09-21 v1 Algebraic Geometry
Abstract
In this work, we study the supersingular locus of the Shimura variety associated to the unitary group 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 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 \`a la Deligne and Lusztig and the study of the admissible set.
Keywords
Cite
@article{arxiv.2309.11290,
title = {On the Rapoport-Zink space for $\mathrm{GU}(2, 4)$ over a ramified prime},
author = {Stefania Trentin},
journal= {arXiv preprint arXiv:2309.11290},
year = {2023}
}