1 December 2015 The geometry of Newton strata in the reduction modulo p of Shimura varieties of PEL type
Paul Hamacher
Duke Math. J. 164(15): 2809-2895 (1 December 2015). DOI: 10.1215/00127094-3328137


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.


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


Received: 20 December 2013; Revised: 6 November 2014; Published: 1 December 2015
First available in Project Euclid: 1 December 2015

zbMATH: 1335.14008
MathSciNet: MR3430453
Digital Object Identifier: 10.1215/00127094-3328137

Primary: 14G35 , 14L05
Secondary: 20G25

Keywords: Newton stratification , Rapoport–Zink space , Shimura variety

Rights: Copyright © 2015 Duke University Press


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Vol.164 • No. 15 • 1 December 2015
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