Abstract
A formally smooth morphism A→B between local noetherian rings gives a formlly smooth morphism AP→BQ for any prime ideal Q if this property holds for B=Â. Regular excellent rings of characteristic p>0 and separated modules of absolute differentials.
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André, M. Localisation de la lissite formelle. Manuscripta Math 13, 297–307 (1974). https://doi.org/10.1007/BF01168230
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DOI: https://doi.org/10.1007/BF01168230