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September 2021 Ideal-adic completion of quasi-excellent rings (after Gabber)
Kazuhiko Kurano, Kazuma Shimomoto
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Kyoto J. Math. 61(3): 707-722 (September 2021). DOI: 10.1215/21562261-2021-0011

Abstract

We give a detailed proof of a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work of Nishimura and Nishimura.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

Dedication

To Professor Jun-ichi Nishimura on the occasion of his 70th birthday

Citation

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Kazuhiko Kurano. Kazuma Shimomoto. "Ideal-adic completion of quasi-excellent rings (after Gabber)." Kyoto J. Math. 61 (3) 707 - 722, September 2021. https://doi.org/10.1215/21562261-2021-0011

Information

Received: 25 November 2016; Revised: 6 September 2018; Accepted: 28 March 2019; Published: September 2021
First available in Project Euclid: 2 June 2021

Digital Object Identifier: 10.1215/21562261-2021-0011

Subjects:
Primary: 13B35
Secondary: 13F25, 13F40

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 3 • September 2021
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