Vol. 8, No. 2, 2014

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On lower ramification subgroups and canonical subgroups

Shin Hattori

Vol. 8 (2014), No. 2, 303–330
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 OK 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 3. As an application, we also prove that the higher canonical subgroup of a level n truncated Barsotti–Tate group G over OK coincides with lower ramification subgroups of G if the Hodge height of G is less than (p 1)pn, 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