On the Jung method in positive characteristic

Piltant, Olivier

Piltant, Olivier

Annales de l'Institut Fourier, Volume 53 (2003) no. 4, p. 1237-1258

Abstract
Résumé

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 $p$

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 $p$ .

MR 2033514 | Zbl 1078.14018

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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