Computating decomposition groups and inertia groups using Newton polygons

Abstract

Newton polygons are powerful tools for computing the decomposition of prime ideals in extension rings. Methods based on Newton polygons have been developed through the work of Ore, Montes, and Nart. Kölle and Schmid obtained a method for determining decomposition groups from Newton polygons and associated data under assumptions introduced by Ore. In this paper, we extend their approach and show how to determine decomposition groups under the weaker assumptions introduced by Montes and Nart, formulated in terms of indices.