2008/04/03 by Stephen Kudla, Kudla, Stephen, Michael Rapoport +1
Mathematics · #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14G35
paper · pdf · doi:10.48550/arxiv.0804.0600
In this new version, suggestions by B. Howard, U. Terstiege, and the referee for Inventiones are taken into account. Also a mistake in the statement of the conjecture at the end of the introduction, that was accidentally added in the galleys for the published version, has been removed
arxiv created 2011/02/17 · arxiv updated 2011/02/18
The supersingular locus in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n-1) over Q is uniformized by a formal scheme \Cal N. In the case when p is inert, we define special cycles Z(x) in \Cal N, associated to a collection x of m `special homomorphisms' with fundamental matrix T in Hermm(OK). When m=n and T is nonsingular, we show that the cycle Z(x) is a union of components of the Ekedahl-Oort stratification, and we give a necessary and sufficient conditions, in terms of T, for Z(x) to be irreducible. When Z(x) is zero dimensional -- in which case it reduces to a single point -- we determine the length of the corresponding local ring by using a variant of the theory of quasi-canonical liftings. We show that this length coincides with the derivative of a representation density for hermitian forms.