# Local monomialization of transcendental extensions

Steven Dale CUTKOSKY^{[1]}

- [1] University of Missouri, department of mathematics, Columbia, MO 65211 (USA)

Annales de l’institut Fourier (2005)

- Volume: 55, Issue: 5, page 1517-1586
- ISSN: 0373-0956

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topDale CUTKOSKY, Steven. "Local monomialization of transcendental extensions." Annales de l’institut Fourier 55.5 (2005): 1517-1586. <http://eudml.org/doc/116225>.

@article{DaleCUTKOSKY2005,

abstract = {Suppose that $R\subset S$ 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) $R\rightarrow R_1$ and $S\rightarrow S_1$ along
$V$ such that $R_1\rightarrow S_1$ 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.},

affiliation = {University of Missouri, department of mathematics, Columbia, MO 65211 (USA)},

author = {Dale CUTKOSKY, Steven},

journal = {Annales de l’institut Fourier},

keywords = {Monomialization; monoidal transform; valuation ring; Morphism; resolution of singularities; local uniformization theorem; toroidalization},

language = {eng},

number = {5},

pages = {1517-1586},

publisher = {Association des Annales de l'Institut Fourier},

title = {Local monomialization of transcendental extensions},

url = {http://eudml.org/doc/116225},

volume = {55},

year = {2005},

}

TY - JOUR

AU - Dale CUTKOSKY, Steven

TI - Local monomialization of transcendental extensions

JO - Annales de l’institut Fourier

PY - 2005

PB - Association des Annales de l'Institut Fourier

VL - 55

IS - 5

SP - 1517

EP - 1586

AB - Suppose that $R\subset S$ 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) $R\rightarrow R_1$ and $S\rightarrow S_1$ along
$V$ such that $R_1\rightarrow S_1$ 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.

LA - eng

KW - Monomialization; monoidal transform; valuation ring; Morphism; resolution of singularities; local uniformization theorem; toroidalization

UR - http://eudml.org/doc/116225

ER -

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