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On the boundary components of central streams in the two slopes case. (English) Zbl 1461.14066

The author introduces a concept called arrowed binary sequence as a generalization of truncated Dieudonné module of level 1. An arrowed binary sequence is a combinatorial object that encodes the information of the Frobenius and Verschiebung of the associated truncated Dieudonné module of level 1. For a Newton polygon \(\xi\), \(H(\xi)\) is the unique minimal \(p\)-divisible group with Newton polygon \(\xi\) (in the sense of F. Oort [Ann. Math. (2) 161, No. 2, 1021–1036 (2005; Zbl 1081.14065)]). Two Newton polygons \(\zeta \prec \xi\) if each point of \(\zeta\) is above or on \(\xi\). Using arrowed binary sequence, the author proves the following theorem:
Theorem: Let \(\xi\) be a Newton polygon consisting of two segments with slopes \(\lambda\) and \(\lambda'\) satisfying \(\lambda < 1/2 < \lambda'\). Let \(X\) be an arbitrary generic specialization of \(H(\xi)\). Then there exists a Newton polygon \(\zeta\) such that \(\zeta \prec \xi\) as well as there exists no Newton polygon \(\eta\) such that \(\zeta \precneqq \eta \precneqq \xi\), and \(H(\zeta)\) appears as a specialization of \(X\).
Reviewer: Xiao Xiao (Utica)

MSC:

14L15 Group schemes
14L05 Formal groups, \(p\)-divisible groups
14K10 Algebraic moduli of abelian varieties, classification

Citations:

Zbl 1081.14065
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References:

[1] F. Oort,Foliations in moduli spaces of abelian varieties,J. Amer. Math. Soc.17(2004), 267-296. · Zbl 1041.14018
[2] F. Oort,Minimalp-divisible groups,Ann. of Math.161(2005), 1021-1036. · Zbl 1081.14065
[3] E.ViehmannandT.Wedhorn,Ekedahl-Oort and Newton strata for Shimura varieties of PEL type,Math. Ann.356(2013), 1493-1550. · Zbl 1314.14047
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