On the equivalence of types

TL;DR

This paper characterizes when two types over a discrete valued field are equivalent by analyzing the data they support, providing a clearer understanding of their relationship to families of prime polynomials.

Contribution

It introduces a new characterization of type equivalence based on the data supported by types, enhancing the understanding of their structure and relationships.

Findings

Provides a criterion for type equivalence in terms of supported data

Clarifies the relationship between types and families of prime polynomials

Improves the theoretical framework for types over valued fields

Abstract

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.