Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.
Soient deux anneaux locaux réguliers, essentiellement de type fini sur un corps de caractéristique zéro. Si est un anneau de valuation du corps des fractions de dominant , nous montrons qu’il existe des suites de transformés monoidaux (éclatements d’idéaux premiers réguliers) et le long de tels que est une application monomiale. Il s’ensuit qu’un morphisme de variétés non singulières peut-être rendu monomial le long d’une valuation après éclatement de sous-variétés non singulières.
Keywords: Monomialization, monoidal transform, valuation ring, Morphism
Mot clés : monomialisation, transformés monoidaux, anneaux de valuation, morphisme
@article{AIF_2005__55_5_1517_0, author = {Dale CUTKOSKY, Steven}, title = {Local monomialization of transcendental extensions}, journal = {Annales de l'Institut Fourier}, pages = {1517--1586}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {5}, year = {2005}, doi = {10.5802/aif.2132}, mrnumber = {2172273}, zbl = {1081.14020}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2132/} }
TY - JOUR AU - Dale CUTKOSKY, Steven TI - Local monomialization of transcendental extensions JO - Annales de l'Institut Fourier PY - 2005 SP - 1517 EP - 1586 VL - 55 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2132/ DO - 10.5802/aif.2132 LA - en ID - AIF_2005__55_5_1517_0 ER -
%0 Journal Article %A Dale CUTKOSKY, Steven %T Local monomialization of transcendental extensions %J Annales de l'Institut Fourier %D 2005 %P 1517-1586 %V 55 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2132/ %R 10.5802/aif.2132 %G en %F AIF_2005__55_5_1517_0
Dale CUTKOSKY, Steven. Local monomialization of transcendental extensions. Annales de l'Institut Fourier, Volume 55 (2005) no. 5, pp. 1517-1586. doi : 10.5802/aif.2132. http://archive.numdam.org/articles/10.5802/aif.2132/
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