The supersingular locus of the Shimura variety for GU(1,n-1) over a ramified prime

Abstract

We analyze the geometry of the supersingular locus of the reduction modulo p of a Shimura variety associated to a unitary similitude group GU(1,n-1) over Q, in the case that p is ramified. We define a stratification of this locus and show that its incidence complex is closely related to a certain Bruhat-Tits simplicial complex. Each stratum is isomorphic to a Deligne-Lusztig variety associated to some symplectic group over F_p and some Coxeter element. The closure of each stratum is a normal projective variety with at most isolated singularities. The results are analogous to those of Vollaard/Wedhorn in the case when p is inert.

A few more corrections, to appear in Math. Zeitschrift

References in corpus (3)

• On the Arithmetic Fundamental Lemma in the minuscule case
• An alternative description of the Drinfeld p-adic half-plane
• On the Hodge-Newton filtration for p-divisible groups with additional structures

Cited by in corpus (4)

• Towards a theory of local Shimura varieties
• Rapoport-Zink spaces for spinor groups
• On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
• Basic loci in Shimura varieties of Coxeter type