Killing wild ramification

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.