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

Let (R, m, k) be a local noetherian domain with field of fractions K and Rν a valuation ring, dominating R (not necessarily birationally). Let ν|K:K* ↠Γ be the restriction of ν to K by definition, ν|K is centred at R. Let R^denote the m‐adic completion of R. In the applications of valuation theory t...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2012-09, Vol.105 (3), p.571-621
Main Authors: Govantes, F. J. Herrera, Acosta, M. A. Olalla, Spivakovsky, M., Teissier, B.
Format: Article
Language:English
Subjects:
Algebra
Constrictions
Mathematical analysis
Positioning
Singularities
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let (R, m, k) be a local noetherian domain with field of fractions K and Rν a valuation ring, dominating R (not necessarily birationally). Let ν|K:K* ↠Γ be the restriction of ν to K by definition, ν|K is centred at R. Let 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 R^ and ν by a suitable extension ν^− to R^/P for a suitably chosen prime ideal P, such that P∩R=(0). The purpose of this paper is to give, assuming that R is excellent, a systematic description of all such extensions ν^− and to identify certain classes of extensions which are of particular interest for applications.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms/pds002