Higher Newton polygons and integral bases

Abstract Let A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A , and K p the completion of K at p . The Montes algorithm factorizes a monic irreducible polynomial f ∈ A [ x ] over K p , and provides essential arithmetic information about the finite extensions of K p determined by the different irreducible factors. In particular, it can be used to compute a p -integral basis of the extension of K determined by f . In this paper we present a new and faster method to compute p -integral bases, based on the use of the quotients of certain divisions with remainder of f that occur along the flow of the Montes algorithm.