Published October 7, 2016 | Version v1
Publication

Extending a valuation centered in a local domain to the formal completion

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Description

Let (R; m; k) be a local noetherian domain with field of fractions K and R_v a valuation ring, dominating R (not necessarily birationally). Let v|K be the restriction of v to K; by definition, v|K is centered at R. Let \hat{R} denote the m-adic completion of R. In the applications of valuation theory to commutative algebra and the study of singularities, one is often induced to replace R by its m-adic completion \hat{R} and v by a suitable extension \hat{v} to \hat{R}/P for a suitably chosen prime ideal P, such that P \cap R = (0). The purpose of this paper is to give, assuming that R is excellent, a systematic description of all such extensions \hat{v} and to identify certain classes of extensions which are of particular interest for applications.

Abstract

Ministerio de Educación y Ciencia

Abstract

Ministerio de Ciencia e Innovación

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Fondo Europeo de Desarrollo Regional

Additional details

Created:
March 27, 2023
Modified:
November 30, 2023