Extending a valuation centered in a local domain to the formal completion
Citation
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
Abstract
Fondo Europeo de Desarrollo Regional
Additional details
- URL
- https://idus.us.es/handle/11441/47165
- URN
- urn:oai:idus.us.es:11441/47165
- Origin repository
- USE