On the Jung method in positive characteristic
[Sur la méthode de Jung en caractéristique positive]
Annales de l'Institut Fourier, Tome 53 (2003) no. 4, pp. 1237-1258.

Soit X ¯ un germe de surface normale d’anneau local 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 R ¯/R, nous étudions l’existence d’une nouvelle paire d’anneaux locaux R ¯ ' /R ' dominant birationnellement R ¯/R, telle que R ' soit régulier et que 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 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

DOI : 10.5802/aif.1978
Classification : 13A18, 14E22, 14J17
Keywords: valuations, coverings, resolution of singularities
Mot clés : valuations, revêtements, résolution des singularités
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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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. http://www.numdam.org/articles/10.5802/aif.1978/

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