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

Kazuhiko Kurano; Kazuma Shimomoto

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We give a detailed proof of a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work of Nishimura and Nishimura.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

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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

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Received: 25 November 2016; Revised: 6 September 2018; Accepted: 28 March 2019; Published: September 2021

First available in Project Euclid: 2 June 2021

MathSciNet: MR4301055

zbMATH: 1471.13025

Digital Object Identifier: 10.1215/21562261-2021-0011

Subjects:

Primary: 13B35

Secondary: 13F25 , 13F40

Keywords: excellent ring , ideal-adic completion , lifting problem , local uniformization , quasi-excellent ring

Abstract

Dedication

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