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

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Título Alternativo: Extending a valuation centred in a local domain to the formal completion
Autor: Herrera Govantes, Francisco Javier
Olalla Acosta, Miguel Ángel
Spivakovsky. Mark
Teissier, Bernard
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2012-09
Publicado en: Proceedings of the London Mathematical Society, 105 (3), 571-621.
Tipo de documento: Artículo
Resumen: 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.
Cita: Herrera Govantes, F.J., Olalla Acosta, M.Á., Spivakovsky. Mark, y Teissier, B. (2012). Extending a valuation centered in a local domain to the formal completion. Proceedings of the London Mathematical Society, 105 (3), 571-621.
Tamaño: 588.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47165

DOI: 10.1112/plms/pds002

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