On the boundary components of central streams in the two slopes case

TL;DR

This paper classifies the boundary components of central streams in the space of p-divisible groups for a specific Newton polygon with two segments, revealing their structure and the generic Newton polygons on these boundaries.

Contribution

It provides a classification of boundary components of central streams for Newton polygons with two segments, one slope below and one above 1/2, and determines their generic Newton polygons.

Findings

Boundary components are classified for the specified Newton polygon.

The generic Newton polygon of each boundary component is determined.

The results deepen understanding of the boundary structure of central streams.

Abstract

In 2004 Oort studied the foliation on the space of $p$-divisible groups. In his theory, special leaves called central streams play an important role. It is still meaningful to investigate central streams, for example, there remain a lot of unknown things on the boundaries of central streams. In this paper, we classify the boundary components of the central stream for a Newton polygon consisting of two segments, where one slope is less than $1/2$ and the other slope is greater than $1/2$. Moreover we determine the generic Newton polygon of each boundary component using this classification.