10 papers
Limits of Amao multiplicities and Epsilon multiplicity
Steven Dale Cutkosky
Let be a -dimensional Noetherian local ring with maximal ideal and be an ideal of . The epsilon multiplicity of is shown in a recent paper of Stephen…
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 wi…
The Proj of the Rees algebra of a graded family of ideals
Steven Dale Cutkosky
In this article we investigate the condition that the Proj of a Rees algebra of a graded family of ideals in a Noetherian local ring is Noetherian. In many cases, the Proj will…
Multiplicities of graded families of ideals on Noetherian local rings
Steven Dale Cutkosky
Let be a -dimensional Noetherian local ring with maximal ideal . In this article, we give a generalization of the multiplicity of an -primary ideal of $…
The Rees algebra and analytic spread of a divisorial filtration
Steven Dale Cutkosky
In this paper we investigate some properties of Rees algebras of divisorial filtrations and their analytic spread. A classical theorem of McAdam shows that the analytic spread of a…
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…