On lower ramification subgroups and canonical subgroups

TL;DR

This paper characterizes ramification subgroups of finite flat group schemes over ramified extensions using Breuil-Kisin classification, and relates canonical subgroups to ramification in Barsotti-Tate groups under certain conditions.

Contribution

It generalizes previous results on ramification subgroups to cases where the group scheme is killed by p^n, linking canonical subgroups with ramification subgroups.

Findings

Describes ramification subgroups via Breuil-Kisin classification.

Shows higher canonical subgroups coincide with ramification subgroups under specific Hodge height conditions.

Extends understanding of ramification in finite flat group schemes over ramified fields.

Abstract

Let p be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fraction field of the Witt ring of k. Let G be a finite flat commutative group scheme over O_K killed by some p-power. In this paper, we prove a description of ramification subgroups of G via the Breuil-Kisin classification, generalizing the author's previous result on the case where G is killed by p>2. As an application, we also prove that the higher canonical subgroup of a level n truncated Barsotti-Tate group G over O_K coincides with lower ramification subgroups of G if the Hodge height of G is less than (p-1)/p^n.