12 citations · 59 across the 35 of their papers we have counts for
6 papers · 2 filters
Almost Mathematics, Kähler differentials and deeply ramified fields
Steven Dale Cutkosky
This article discusses ramification and the structure of relative Kähler differentials of extensions of valued fields. We begin by surveying the theory developed in recent work wit…
Generating sequences of valuations on simple extensions of domains
Razieh Ahmadian, Steven Dale Cutkosky
Suppose that is a valued field, is a monic and irreducible polynomial and is an extension of valued fields, where . Let be a loc…
Kähler differentials of extensions of valuation rings and deeply ramified fields
Steven Dale Cutkosky, Franz-Viktor Kuhlmann
Assume that is a finite Galois extension of a valued field . We give an explicit construction of the valuation ring of as an -algebr…
Epsilon multiplicity and analytic spread of filtrations
Steven Dale Cutkosky, Parangama Sarkar
We extend the epsilon multiplicity of ideals defined by Ulrich and Validashti to epsilon multiplicity of filtrations, and show that under mild assumptions this multiplicity exists…
On the computation of Kähler differentials and characterizations of Galois extensions with independent defect
Steven Dale Cutkosky, Franz-Viktor Kuhlmann, Anna Rzepka
For important cases of algebraic extensions of valued fields, we develop presentations of the associated Kähler differentials of the extensions of their valuation rings. We compute…
A counterexample to strong local monomialization in a tower of two independent defect Artin-Schreier extensions
Steven Dale Cutkosky
We give an example of an extension of two dimensional regular local rings in a tower of two independent defect Artin-Schreier extensions for which strong local monomialization does…