On the compositum of wildly ramified extensions

TL;DR

This paper calculates ramification filtrations in certain wildly ramified local field extensions and applies these results to make progress on Abhyankar's Inertia conjecture.

Contribution

It provides explicit computations of ramification filtrations for specific wildly ramified extensions and advances understanding of Abhyankar's Inertia conjecture.

Findings

Computed ramification filtration for $p^2$-cyclic extensions.

Determined ramification in compositum of $p$-cyclic and $p^2$-cyclic extensions.

Made partial progress on Abhyankar's Inertia conjecture.

Abstract

We compute the ramification filtration on wildly ramified $p^2$-cyclic extensions of local fields of characteristic $p$. The ramification filtration on the compositum of two $p$-cyclic and $p^2$-cyclic extensions are also computed. As an application, some partial results towards Abhyankar's Inertia conjecture has been proved.