Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 15 (2015), 2809-2895.
The geometry of Newton strata in the reduction modulo of Shimura varieties of PEL type
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.
Duke Math. J. Volume 164, Number 15 (2015), 2809-2895.
Received: 20 December 2013
Revised: 6 November 2014
First available in Project Euclid: 1 December 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 14L05: Formal groups, $p$-divisible groups [See also 55N22]
Secondary: 20G25: Linear algebraic groups over local fields and their integers
Hamacher, Paul. The geometry of Newton strata in the reduction modulo $p$ of Shimura varieties of PEL type. Duke Math. J. 164 (2015), no. 15, 2809--2895. doi:10.1215/00127094-3328137. https://projecteuclid.org/euclid.dmj/1448980435