On the boundary components of central streams in the two slopes case (Q783762)

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 \textit{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 \(X\).