On the equivalence of types

Types over a discrete valued field $(K,v)$ are computational objects that parameterize certain families of monic irreducible polynomials in $K_v[x]$, where $K_v$ is the completion of $K$ at $v$. Two types are considered to be equivalent if they encode the same family of prime polynomials. In this paper, we characterize the equivalence of types in terms of certain data supported by them

Genetics of polynomials over local fields

Let $(K,v)$ be a discrete valued field with valuation ring \oo, and let \oo_v be the completion of \oo with respect to the $v$-adic topology. In this paper we discuss the advantages of manipulating polynomials in \oo_v[x] in a computer by means of OM representations of prime (monic and irreducible) polynomials. An OM representation supports discrete data characterizing the Okutsu equivalence class of the prime polynomial. These discrete parameters are a kind of DNA sequence common to all individuals in the same Okutsu class, and they contain relevant arithmetic information about the polynomial and the extension of $K_v$ that it determines.Comment: revised according to suggestions by a refere

Okutsu-montes representations of prime ideals of one-dimensional integral closures

This is a survey on Okutsu-Montes representations of prime ideals of certain one-dimensional integral closures. These representations facilitate the computational resolution of several arithmetic tasks concerning prime ideals of global fields