Successive extensions of minimal [formula omitted]-divisible groups

Abstract

We study truncated Barsotti–Tate groups of level one ( BT 1 ) and their extensions to p -divisible groups. Firstly we show that any BT 1 contains a certain minimal BT 1 as a non-zero subgroup scheme. This proves that any BT 1 is written as a successive extension of minimal BT 1 ’s. Secondly we prove that any successive extension of minimal BT 1 ’s which is a BT 1 can be extended to a certain successive extension of minimal p -divisible groups. As an application, we determine the optimal upper bound of the last Newton slopes of p -divisible groups with a given isomorphism type of p -kernel.