On the Jung method in positive characteristic

[Sur la méthode de Jung en caractéristique positive]

Piltant, Olivier

Annales de l'Institut Fourier, Tome 53 (2003), p. 1237-1258 / Harvested from Numdam

Résumé

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

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 $p>0$. 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 $p$

Détail

Publié le : 2003-01-01

MR 2033514 | Zbl 1078.14018

DOI : https://doi.org/10.5802/aif.1978
Classification:  13A18,  14E22,  14J17
Mots clés: valuations, revêtements, résolution des singularités

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