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)


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


Zbl 1081.14065
Full Text: DOI arXiv Euclid


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.