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arXiv · 1609.09246

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

Kazuhiko Kurano·Kazuma Shimomoto
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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In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura.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).

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Kazuhiko Kurano, Kazuma Shimomoto. 2016-09-29. Ideal-adic completion of quasi-excellent rings (after Gabber). https://doi.org/10.1215/21562261-2021-0011

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