Ramification of local fields with imperfect residue fields III

TL;DR

This paper investigates the structure of logarithmic ramification groups in local fields with imperfect residue fields, revealing their connection to differential forms and showing they are annihilated by the residue characteristic.

Contribution

It extends the understanding of ramification groups in local fields with imperfect residue fields, linking their characters to differential forms and clarifying their annihilation properties.

Findings

Logarithmic ramification groups are killed by the residue characteristic.

Characters of these groups are described via differential forms.

Provides new insights into ramification in imperfect residue fields.

Abstract

The graded quotients of the logarithmic ramification groups of a local field of mixed characteristic is killed by the residue characteristic. Its characters are described by differential forms.