Characterizing finitely generated fields by a single field axiom
P Dittmann, F Pop - Annals of Mathematics, 2023 - projecteuclid.org
We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely
generated fields. That is, we show that for every field in this class, there is a first-order …
generated fields. That is, we show that for every field in this class, there is a first-order …
Local uniformization of Abhyankar valuations
SD Cutkosky - Michigan Mathematical Journal, 2022 - projecteuclid.org
We prove local uniformization of Abhyankar valuations of an algebraic function field K over a
ground field k. Our result generalizes the proof of this result, with the additional assumption …
ground field k. Our result generalizes the proof of this result, with the additional assumption …
Elimination of ramification II: Henselian rationality
FV Kuhlmann - Israel Journal of Mathematics, 2019 - Springer
We prove in arbitrary characteristic that an immediate valued algebraic function field F of
transcendence degree 1 over a tame field K is contained in the henselization of K (x) for a …
transcendence degree 1 over a tame field K is contained in the henselization of K (x) for a …
Essentially finite generation of valuation rings in terms of classical invariants
SD Cutkosky, J Novacoski - Mathematische Nachrichten, 2021 - Wiley Online Library
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 extension ω …
classical invariants. More specifically, we consider a valued field (K, ν) and an extension ω …
Generators for extensions of valuation rings
J Novacoski - arXiv preprint arXiv:2401.00182, 2023 - arxiv.org
For a finite valued field extension $(L/K, v) $ we describe the problem of find sets of
generators for the corresponding extension $\mathcal O_L/\mathcal O_K $ of valuation …
generators for the corresponding extension $\mathcal O_L/\mathcal O_K $ of valuation …
Essential finite generation of extensions of valuation rings
R Datta - Mathematische Nachrichten, 2023 - Wiley Online Library
Given a generically finite local extension of valuation rings V⊂ WV⊂W, the question of
whether W is the localization of a finitely generated V‐algebra is significant for approaches …
whether W is the localization of a finitely generated V‐algebra is significant for approaches …
Essential finite generation of valuation rings in characteristic zero algebraic function fields
SD Cutkosky - Algebra & Number Theory, 2022 - msp.org
Let K be a characteristic zero algebraic function field with a valuation ν. Let L be a finite
extension of K and ω be an extension of ν to L. We establish that the valuation ring V ω of ω …
extension of K and ω be an extension of ν to L. We establish that the valuation ring V ω of ω …
Defects of algebraic function fields, completion defects and defect quotients
FV Kuhlmann, A Naseem - arXiv preprint arXiv:1304.0198, 2013 - arxiv.org
The {\it defect}(also called {\it ramification deficiency}) of valued field extensions is a major
stumbling block in deep open problems of valuation theory in positive characteristic. For a …
stumbling block in deep open problems of valuation theory in positive characteristic. For a …
Algebra & Number Theory
SD Cutkosky - ALGEBRA AND NUMBER THEORY, 2017 - projecteuclid.org
Suppose that R is a 2-dimensional excellent local domain with quotient field K, K∗ is a finite
separable extension of K and S is a 2-dimensional local domain with quotient field K∗ such …
separable extension of K and S is a 2-dimensional local domain with quotient field K∗ such …