Ideal-adic completion of quasi-excellent rings (after Gabber)

Abstract

In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura. As a corollary, we establish that an ideal-adic completion of an excellent (resp. quasi-excellent) ring is excellent (resp. quasi-excellent).

The final version, accepted by Kyoto J. Math

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