Killing wild ramification

TL;DR

This paper analyzes the inertia groups in wildly ramified Galois covers, showing how to reduce the p-part of the inertia group under specific ramification conditions, advancing understanding of ramification behavior in algebraic covers.

Contribution

It introduces a method to reduce the p-part of inertia groups in Galois covers of the projective line with specific ramification jumps, using compositum computations.

Findings

Computed inertia groups of wildly ramified Galois covers.

Established conditions for reducing the p-part of inertia groups.

Demonstrated the impact of ramification jumps on inertia group structure.

Abstract

We compute the inertia group of the compositum of wildly ramified Galois covers. It is used to show that even the $p$-part of the inertia group of a Galois cover of $\PP^1$ branched only at infinity can be reduced if there is a jump in the ramification filtration at two (in the lower numbering) and certain linear disjointness statement holds.