On the Jung method in positive characteristic

Olivier Piltant[1]

  • [1] Université de Versailles, LAMA--UMR 8100 du CNRS, 45 avenue des États-Unis, Bâtiment Fermat, 78035 Versailles (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 4, page 1237-1258
  • ISSN: 0373-0956

Abstract

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Let X ¯ be a germ of normal surface with local ring R ¯ covering a germ of regular surface X with local ring R of characteristic p > 0 . Given an extension of valuation rings W / V birationally dominating R ¯ / R , we study the existence of a new such pair of local rings R ¯ ' / R ' birationally dominating R ¯ / R , such that R ' is regular and R ¯ ' has only toric singularities. This is achieved when W / V is defectless or when [ W : V ] is equal to p

How to cite

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Piltant, Olivier. "On the Jung method in positive characteristic." Annales de l’institut Fourier 53.4 (2003): 1237-1258. <http://eudml.org/doc/116066>.

@article{Piltant2003,
abstract = {Let $\overline\{X\}$ be a germ of normal surface with local ring $\overline\{R\}$ covering a germ of regular surface $X$ with local ring $R$ of characteristic $p&gt;0$. Given an extension of valuation rings $W/V$ birationally dominating $\overline\{R\}/R$, we study the existence of a new such pair of local rings $\overline\{R\}^\{\prime \}/R^\{\prime \}$ birationally dominating $\overline\{R\}/R$, such that $R^\{\prime \}$ is regular and $\overline\{R\}^\{\prime \}$ has only toric singularities. This is achieved when $W/V$ is defectless or when $[W:V ]$ is equal to $p$},
affiliation = {Université de Versailles, LAMA--UMR 8100 du CNRS, 45 avenue des États-Unis, Bâtiment Fermat, 78035 Versailles (France)},
author = {Piltant, Olivier},
journal = {Annales de l’institut Fourier},
keywords = {valuations; coverings; resolution of singularities},
language = {eng},
number = {4},
pages = {1237-1258},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the Jung method in positive characteristic},
url = {http://eudml.org/doc/116066},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Piltant, Olivier
TI - On the Jung method in positive characteristic
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 4
SP - 1237
EP - 1258
AB - Let $\overline{X}$ be a germ of normal surface with local ring $\overline{R}$ covering a germ of regular surface $X$ with local ring $R$ of characteristic $p&gt;0$. Given an extension of valuation rings $W/V$ birationally dominating $\overline{R}/R$, we study the existence of a new such pair of local rings $\overline{R}^{\prime }/R^{\prime }$ birationally dominating $\overline{R}/R$, such that $R^{\prime }$ is regular and $\overline{R}^{\prime }$ has only toric singularities. This is achieved when $W/V$ is defectless or when $[W:V ]$ is equal to $p$
LA - eng
KW - valuations; coverings; resolution of singularities
UR - http://eudml.org/doc/116066
ER -

References

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