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On lower ramification subgroups and canonical subgroups. (English) Zbl 1315.11096

The author gives a description of ramification subgroups of a finite flat commutative group schemes over the integer ring of a totally ramified extension of the fraction field of the Witt ring of a perfect field of characteristic \(p\), a rational prime number. He also proves results related to the Barsotti-Tate group.
Author’s 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 \(\mathcal G\) be a finite flat commutative group scheme over \(\mathcal O_K\) killed by some \(p\)-power. In this paper, we prove a description of ramification subgroups of \(\mathcal G\) via the Breuil-Kisin classification, generalizing the author’s previous result on the case where \(\mathcal G\) is killed by \(p \geq 3\) [J. Number Theory 132, No. 10, 2084–2102 (2012; Zbl 1270.14021)]. As an application, we also prove that the higher canonical subgroup of a level n truncated Barsotti-Tate group \(\mathcal G\) over \(\mathcal O_K\) coincides with lower ramification subgroups of \(\mathcal G\) if the Hodge height of \(\mathcal G\) is less than \((p - 1)/p^n\), and the existence of a family of higher canonical subgroups improving a previous result of the author [Math. Z. 274, No. 3–4, 933–953 (2013; Zbl 1332.14058)].

MSC:

11S23 Integral representations
14L05 Formal groups, \(p\)-divisible groups
14L15 Group schemes
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