## 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

### Keywords:

$$p$$-divisible group; deformation space; Newton polygons

Zbl 1081.14065
Full Text:

### 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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