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On lower ramification subgroups and canonical subgroups (1208.5326v2)

Published 27 Aug 2012 in math.NT and math.AG

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)/pn.

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