The geometry of Newton strata in the reduction modulo p of Shimura varieties of PEL type

Abstract

In this paper we study the Newton stratification on the reduction of Shimura varieties of PEL type with hyperspecial level structure. Our main result is a formula for the dimension of Newton strata and the description of their closure, where the dimension formula was conjectured by Chai. As a key ingredient of its proof we calculate the dimension of some Rapoport–Zink spaces. Our result yields a dimension formula, which was conjectured by Rapoport (up to a minor correction).

As an interesting application to deformation theory, we determine the dimension and closure of Newton strata on the algebraization of the deformation space of a Barsotti–Tate group with (P)EL structure. Our result on the closure of a Newton stratum generalizes conjectures of Grothendieck and Koblitz.