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.
"The geometry of Newton strata in the reduction modulo of Shimura varieties of PEL type." Duke Math. J. 164 (15) 2809 - 2895, 1 December 2015. https://doi.org/10.1215/00127094-3328137