On the Jung method in positive characteristic

Piltant, Olivier

doi:10.5802/aif.1978

On the Jung method in positive characteristic
[Sur la méthode de Jung en caractéristique positive]

Piltant, Olivier 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, Tome 53 (2003) no. 4, pp. 1237-1258.

Résumé
Abstract

Soit $\bar{X}$ un germe de surface normale d’anneau local $\bar{R}$ revêtant un germe de surface régulière $X$ d’anneau local $R$ de caractéristique $p > 0$ . Étant donnée une extension d’anneaux de valuation $W / V$ dominant birationnellement $\bar{R} / R$ , nous étudions l’existence d’une nouvelle paire d’anneaux locaux ${\bar{R}}^{'} / R^{'}$ dominant birationnellement $\bar{R} / R$ , telle que $R^{'}$ soit régulier et que ${\bar{R}}^{'}$ n’ait que des singularités toriques. Cette dernière est construite lorsque $W / V$ est sans défaut ou lorsque le degré $[W : V]$ est $p$ .

Let $\bar{X}$ be a germ of normal surface with local ring $\bar{R}$ 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 $\bar{R} / R$ , we study the existence of a new such pair of local rings ${\bar{R}}^{'} / R^{'}$ birationally dominating $\bar{R} / R$ , such that $R^{'}$ is regular and ${\bar{R}}^{'}$ has only toric singularities. This is achieved when $W / V$ is defectless or when $[W : V]$ is equal to $p$

MR Zbl

DOI : 10.5802/aif.1978

Classification : 13A18, 14E22, 14J17
Keywords: valuations, coverings, resolution of singularities
Mot clés : valuations, revêtements, résolution des singularités

Affiliations des auteurs :

Piltant, Olivier ¹

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

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     title = {On the {Jung} method in positive characteristic},
     journal = {Annales de l'Institut Fourier},
     pages = {1237--1258},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {53},
     number = {4},
     year = {2003},
     doi = {10.5802/aif.1978},
     zbl = {1078.14018},
     mrnumber = {2033514},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1978/}
}

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Piltant, Olivier. On the Jung method in positive characteristic. Annales de l'Institut Fourier, Tome 53 (2003) no. 4, pp. 1237-1258. doi : 10.5802/aif.1978. https://aif.centre-mersenne.org/articles/10.5802/aif.1978/

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