On the Jung method in positive characteristic
Annales de l'Institut Fourier, Volume 53 (2003) no. 4, p. 1237-1258
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
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.
DOI : https://doi.org/10.5802/aif.1978
Classification:  13A18,  14E22,  14J17
Keywords: valuations, coverings, resolution of singularities
@article{AIF_2003__53_4_1237_0,
     author = {Piltant, Olivier},
     title = {On the Jung method in positive characteristic},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {4},
     year = {2003},
     pages = {1237-1258},
     doi = {10.5802/aif.1978},
     zbl = {1078.14018},
     mrnumber = {2033514},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_4_1237_0}
}
Piltant, Olivier. On the Jung method in positive characteristic. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1237-1258. doi : 10.5802/aif.1978. http://www.numdam.org/item/AIF_2003__53_4_1237_0/

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