%0 Journal Article
%T The analogue of Izumi's Theorem for Abhyankar valuations
%+ Institut de Mathématiques de Marseille (I2M)
%+ Institut de Mathématiques de Toulouse UMR5219 (IMT)
%A Rond, Guillaume
%A Spivakovsky, Mark
%Z 16 pages
%< avec comité de lecture
%@ 0024-6107
%J Journal of the London Mathematical Society
%I London Mathematical Society ; Wiley
%V 90
%N 3
%P 725-740
%8 2014
%D 2014
%Z 1404.4885
%Z Primary: 13A18. Secondary: 13A15, 16W60
%Z Mathematics [math]/Commutative Algebra [math.AC]Journal articles
%X A well known theorem of Shuzo Izumi, strengthened by David Rees, asserts that all the divisorial valuations centered in an analytically irreducible local noetherian ring are linearly comparable to each other. In the present paper we generalize this theorem to the case of Abhyankar valuations with archimedian value semigroup. Indeed, we prove that in a certain sense linear equivalence of topologies characterizes Abhyankar valuations with archimedian semigroups, centered in analytically irreducible local noetherian rings. Then we show that some of the classical results on equivalence of topologies in noetherian rings can be strengthened to include linear equivalence of topologies. We also prove a new comparison result between the Krull topology and the topology defined by the symbolic powers of an arbitrary ideal.
%G English
%2 https://hal.science/hal-00980846/document
%2 https://hal.science/hal-00980846/file/struct_new2.pdf
%L hal-00980846
%U https://hal.science/hal-00980846
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ UNIV-AMU
%~ INSA-TOULOUSE
%~ EC-MARSEILLE
%~ IMT
%~ I2M
%~ I2M-2014-
%~ UT1-CAPITOLE
%~ INSA-GROUPE
%~ ANR
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP