Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fields

TL;DR

This paper establishes a natural isomorphism between the ramification subgroups of finite flat group schemes over local fields of equal and mixed characteristic, linking their structures via Kisin modules.

Contribution

It demonstrates a correspondence between ramification subgroups of group schemes in different characteristics through Kisin modules, extending ramification theory.

Findings

Isomorphism of ramification subgroups in equal and mixed characteristic cases

Connection established via Kisin modules

Enhances understanding of ramification in finite flat group schemes

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.