NEWTON POLYGONS AND p-INTEGRAL BASES OF QUARTIC NUMBER FIELDS

Abstract

Let p be a prime number. In this paper we use an old technique of Ø. Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by p-regular equations. To illustrate the potential applications of this construction, we derive from this result an explicit description of a p-integral basis of an arbitrary quartic field in terms of a defining equation.