English

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

Commutative Algebra 2023-02-22 v2 Algebraic Geometry

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In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura.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

Keywords

Cite

@article{arxiv.1609.09246,
  title  = {Ideal-adic completion of quasi-excellent rings (after Gabber)},
  author = {Kazuhiko Kurano and Kazuma Shimomoto},
  journal= {arXiv preprint arXiv:1609.09246},
  year   = {2023}
}

Comments

The final version, accepted by Kyoto J. Math