Duke Mathematical Journal

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

Paul Hamacher

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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.

Article information

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

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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

Newton stratification Shimura variety Rapoport–Zink space


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

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