Let be a germ of normal surface with local ring covering a germ of regular surface with local ring of characteristic . Given an extension of valuation rings birationally dominating , we study the existence of a new such pair of local rings birationally dominating , such that is regular and has only toric singularities. This is achieved when is defectless or when is equal to
Soit un germe de surface normale d’anneau local revêtant un germe de surface régulière d’anneau local de caractéristique . Étant donnée une extension d’anneaux de valuation dominant birationnellement , nous étudions l’existence d’une nouvelle paire d’anneaux locaux dominant birationnellement , telle que soit régulier et que n’ait que des singularités toriques. Cette dernière est construite lorsque est sans défaut ou lorsque le degré est .
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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