Local monomialization of transcendental extensions
Annales de l'Institut Fourier, Volume 55 (2005) no. 5, p. 1517-1586
Suppose that RS are regular local rings which are essentially of finite type over a field k of characteristic zero. If V is a valuation ring of the quotient field K of S which dominates S, then we show that there are sequences of monoidal transforms (blow ups of regular primes) RR 1 and SS 1 along V such that R 1 S 1 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 RS deux anneaux locaux réguliers, essentiellement de type fini sur un corps k de caractéristique zéro. Si V est un anneau de valuation du corps des fractions K de S dominant S, nous montrons qu’il existe des suites de transformés monoidaux (éclatements d’idéaux premiers réguliers) RR 1 et SS 1 le long de V tels que R 1 S 1 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.
DOI : https://doi.org/10.5802/aif.2132
Classification:  14E,  13A,  13B
Keywords: Monomialization, monoidal transform, valuation ring, Morphism
@article{AIF_2005__55_5_1517_0,
     author = {Dale CUTKOSKY, Steven},
     title = {Local monomialization of transcendental extensions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {5},
     year = {2005},
     pages = {1517-1586},
     doi = {10.5802/aif.2132},
     mrnumber = {2172273},
     zbl = {1081.14020},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/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. https://aif.centre-mersenne.org/item/AIF_2005__55_5_1517_0/

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