Artículo
Extending a valuation centered in a local domain to the formal completion
Título alternativo | Extending a valuation centred in a local domain to the formal completion |
Autor/es | Herrera Govantes, Francisco Javier
Olalla Acosta, Miguel Ángel Spivakovsky, Mark Teissier, Bernard |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2012-09 |
Fecha de depósito | 2016-10-07 |
Publicado en |
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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 ... 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. |
Identificador del proyecto | MTM2007-66929
MTM2010-19298 |
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. |
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