On lower ramification subgroups and canonical subgroups

Hattori, Shin

doi:10.2140/ant.2014.8.303

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On lower ramification subgroups and canonical subgroups

Shin Hattori

Vol. 8 (2014), No. 2, 303–330

DOI: 10.2140/ant.2014.8.303

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 $p \geq 3$ . 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 $(p - 1) ∕ p^{n}$ , and the existence of a family of higher canonical subgroups improving a previous result of the author.

Keywords

finite flat group scheme, Breuil–Kisin module, canonical subgroup

Mathematical Subject Classification 2010

Primary: 11S23

Secondary: 14L05, 14L15

Milestones

Received: 12 October 2012

Revised: 18 November 2013

Accepted: 19 November 2013

Published: 18 May 2014

Authors

Shin Hattori
Faculty of Mathematics Kyushu University 744 Motooka, Nishi-ku Fukuoka 819-0395 Japan

Vol. 8, No. 2, 2014