J. Novacoski

activity

20122026

most citedHenselian Elements

7 citations · 13 across the 26 of their papers we have counts for

collaborators

34 papers

math.AC2026

Ramification invariants of pure extensions

Josnei Novacoski

We study ramification invariants of finite separable extensions of valued fields that are pure on a primitive element. In the immediate unibranched case, we prove that the extended…

math.AC2026

Ramification ideals for products of pure subgroups

Josnei Novacoski

We study ramification ideals of finite Galois extensions of henselian valued fields whose Galois groups are products of pure subgroups. We give a criterion showing that the ideals…

math.AC2026

On topologies on the space of valuations and the valuative tree

Vinicius Manfredini, Josnei Novacoski, Caio Henrique Silva de Souza

In this paper, we discuss topological aspects of the space of valuations $V$ and the valuative tree $T (v, Λ)$ . We present a relation between the weak tree topolog…

math.AC2025

Purity and distances between conjugates of elements over henselian valued fields

Arpan Dutta, Josnei Novacoski

For a henselian valued field $(K, v)$ and a separable-algebraic element $a \in K ∖ K$ , we consider the set $S_K(a):= \{ v(a-a^\prime) \mid a^\prime\neq a \text{ is a…

math.AC2025

On the distances of an element to its conjugates

Josnei Novacoski

For a valued field $(K, v)$ , with a fixed extension of $v$ to the algebraic closure $K$ of $K$ , and an algebraic element $θ \in K$ , we study the possible values of…

math.AC2025

Valuation rings in simple algebraic extensions of valued fields

Josnei Novacoski, Mark Spivakovsky

Consider a simple algebraic valued field extension $(L / K, v)$ and denote by $\VR_L$ and $\VR_K$ the corresponding valuation rings. The main goal of this paper is to present, under c…

math.AC2025

Depth of extensions of valuations

Josnei Novacoski, Enric Nart

In this paper we develop the theory of the depth of a simple algebraic extension of valued fields $(L / K, v)$ . This is defined as the minimal number of augmentations appearing in som…

math.AC2024

A topological approach to key polynomials

Enric Nart, Josnei Novacoski, Giulio Peruginelli

In this paper we present characterizations of the sets of key polynomials and abstract key polynomials for a valuation $μ$ of $K (x)$ , in terms of (ultrametric) balls in the algebra…

math.AC2023

Generators for extensions of valuation rings

Josnei Novacoski

For a finite valued field extension $(L / K, v)$ we describe the problem of finding sets of generators for the corresponding extension $\VR_L/\VR_K$ of valuation rings. The main tool…

math.AC2023

Kähler differentials, pure extensions and minimal key polynomials

Josnei Novacoski, Mark Spivakovsky

The main object of study in this paper is the module $Ω$ of Kähler differentials of an extension of valuation rings. We show that in the case of pure extensions $Ω$ has a very good…

math.AC2023★ 1 cited

Minimal limit key polynomials

Enric Nart, Josnei Novacoski

In this paper, we extend the theory of minimal limit key polynomials of valuations on the polynomial ring $\kx$. Minimal key polynomials are useful to describe, for instance, the d…

math.AC2023

Parametrizations of subsets of the space of valuations

Josnei Antonio Novacoski, Caio Henrique Silva de Souza

In this paper we present different ways to parametrize subsets of the space of valuations on $K [x]$ extending a given valuation on $K$ . We discuss the methods using pseudo-Cauchy s…

math.AC2023

The module of Kähler differentials for extensions of valuation rings

Josnei Novacoski, Mark Spivakovsky

The main goal of this paper is to describe the module of Kähler differentials for an extension of valuation rings. More precisely, we consider a simple algebraic valued field exten…

math.AC2022

A characterization for the defect of rank one valued field extensions

Josnei Novacoski

In this paper we present a characterization for the defect of a simple algebraic extension of rank one valued fields using the key polynomials that define the valuation. As a parti…

math.AG2022

Geometric parametrization of valuations on a polynomial ring

Enric Nart, Josnei Novacoski

We extend and prove a conjecture of Benguş-Lasnier on the parametrization of valuations on a polynomial ring by certain spaces of diskoids.

math.AC2022

The defect formula

Josnei Novacoski, Enric Nart

In this paper we present a characterization for the defect of a simple algebraic extensions of valued fields. This characterization generalizes the known result for the henselian c…

math.AC2022

On stable and fixed polynomials

J Novacoski, M. Spivakovsky

Let $ν$ be a rank one valuation on $K [x]$ and $Ψ_{n}$ the set of key polynomials for $ν$ of degree $n \in N$ . We discuss the concepts of being $Ψ_{n}$ -stable and $(Ψ_{n}, Q)$ -fixed. We dis…

math.AC2021

Valuations on $K [x]$ approaching a fixed irreducible polynomial

Josnei Novacoski, Matheus dos S. Barnabe

For a fixed irreducible polynomial $F$ we study the set $V_{F}$ of all valuations on $K [x]$ bounded by valuations whose support is $(F)$ . The first main result presents a ch…

math.AC2021★ 2 cited

On truncations of valuations

Josnei Antonio Novacoski, Caio Henrique Silva de Souza

In this paper we study the truncation $ν_{q}$ of a valuation $ν$ on a polynomial $q$ . It is known that when $q$ is a key polynomial, then $ν_{q}$ is a valuation. It is also known that…

math.AC2020

Limit key polynomials as $p$ -polynomials

Michael de Moraes, Josnei Novacoski

The main goal of this paper is to characterize limit key polynomials for a valuation $ν$ on $K [x]$ . We consider the set $Ψ_{α}$ of key polynomials for $ν$ of degree $α$ . We set $p$ b…

math.AC2020★ 1 cited

Generating sequences and key polynomials

Matheus dos Santos Barnabé, Josnei Novacoski

The main goal of this paper is to study the different definitions of generating sequences appearing in the literature. We present these definitions and show that under certain situ…

math.AC2020

On MacLane-Vaquié key polynomials

Josnei Novacoski

One of the main goals of this paper is to present the relation of limit key polynomials and limit MacLane-Vaquié key polynomials. This is a continuation of the work started in a pa…

math.AC2019

Perron transforms and Hironaka's game

Michael de Moraes, Josnei Novacoski

In this paper we present a matricial result that generalizes Hironaka's game and Perron transforms simultaneously. We also show how one can deduce the various forms in which the al…

math.AC2019

Essentially finite generation of valuation rings in terms of classical invariants

Steven Dale Cutkosky, Josnei Novacoski

The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field $(K, ν)$ and an extens…

Ramification invariants of pure extensions

Ramification ideals for products of pure subgroups

On topologies on the space of valuations and the valuative tree

Purity and distances between conjugates of elements over henselian valued fields

On the distances of an element to its conjugates

Valuation rings in simple algebraic extensions of valued fields

Depth of extensions of valuations

A topological approach to key polynomials

Generators for extensions of valuation rings

Kähler differentials, pure extensions and minimal key polynomials

Minimal limit key polynomials

Parametrizations of subsets of the space of valuations

The module of Kähler differentials for extensions of valuation rings

A characterization for the defect of rank one valued field extensions

Geometric parametrization of valuations on a polynomial ring

The defect formula

On stable and fixed polynomials

Valuations on K[x] approaching a fixed irreducible polynomial

On truncations of valuations

Limit key polynomials as p-polynomials

Generating sequences and key polynomials

On MacLane-Vaquié key polynomials

Perron transforms and Hironaka's game

Essentially finite generation of valuation rings in terms of classical invariants

Valuations on $K [x]$ approaching a fixed irreducible polynomial

Limit key polynomials as $p$ -polynomials