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 and the Newton stratification on the deformation space of a Barsotti-Tate group with PEL structure. Our main result is a formula for the dimension of Newton strata and the description their closure in each of the two cases. Furthermore, we calculate the dimension of some Rapoport-Zink spaces as an intermediate result.

56 pages; v2: corrected some typos, gave more detailed introduction and added a sketch for the idea behind the definition of "numerical dimension" at the beginning of section 10

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• Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits