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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …