The ramification filtration in certain $p$-extensions

TL;DR

This paper extends a recent result on ramification filtration from function fields of prime characteristic to local fields of mixed characteristic, offering a more natural and concise local proof applicable in both cases.

Contribution

It provides a purely local, conceptual, and shorter proof of the ramification filtration result, valid for both equicharacteristic and mixed characteristic local fields.

Findings

The result applies to local fields of mixed characteristic.

The proof is purely local and conceptual.

The method is shorter and more natural.

Abstract

We show that the recent result of Casta\~neda and Wu about the ramification filtration in certain $p$-extensions of function fields of prime characteristic $p$ is equally valid over local fields of mixed characteristic $(0,p)$. Apart from being applicable to both equicharacteristic and mixed characteristic cases, our method has the advantage of being purely local, purely conceptual, more natural, and much shorter.