On Ramification Filtrations and p-adic Differential Equations, II: mixed characteristic case

TL;DR

This paper extends the Hasse-Arf theorem to mixed characteristic fields with imperfect residue fields, providing new insights into ramification filtrations and their applications to finite flat group schemes.

Contribution

It proves a Hasse-Arf theorem for arithmetic ramification filtrations in mixed characteristic, addressing cases with imperfect residue fields and extending previous results.

Findings

Hasse-Arf theorem established for most mixed characteristic cases

Application to filtrations on finite flat group schemes

Partial results in absolutely unramified and p=2 logarithmic cases

Abstract

Let K be a complete discretely valued field of mixed characteristic (0, p) with possibly imperfect residue field. We prove a Hasse-Arf theorem for the arithmetic ramification filtrations on G_K, except possibly in the absolutely unramified and non-logarithmic case, or p=2 and logarithmic case. As an application, we obtain a Hasse-Arf theorem for filtrations on finite flat group schemes over O_K.