Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fields
arXiv:1007.3094 · doi:10.1016/j.jnt.2012.04.003
Abstract
Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and k[[u]], respectively. In this paper, we show the upper and the lower ramification subgroups of G and H in the sense of Abbes-Saito are naturally isomorphic to each other when they are associated to the same Kisin module.
22 pages; refereed version; Lemma 4.2 corrected; proof of Proposition 4.4 simplified; Remark 4.7 added; other minor revisions