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arXiv · 2309.11290

On the Rapoport-Zink space for $\mathrm{GU}(2, 4)$ over a ramified prime

Stefania Trentin
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Abstract

In this work, we study the supersingular locus of the Shimura variety associated to the unitary group $\mathrm{GU}(2,4)$ 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 \`a la Deligne and Lusztig and the study of the admissible set.

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Stefania Trentin. 2023-09-20. On the Rapoport-Zink space for $\mathrm{GU}(2, 4)$ over a ramified prime. https://arxiv.org/abs/2309.11290

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