1. Ideal-adic completion of quasi-excellent rings (after Gabber)
- Author
-
Kazuhiko Kurano and Kazuma Shimomoto
- Subjects
Ring (mathematics) ,Pure mathematics ,Mathematics::Commutative Algebra ,010102 general mathematics ,Excellent ring ,Commutative Algebra (math.AC) ,Mathematics - Commutative Algebra ,01 natural sciences ,Mathematics - Algebraic Geometry ,Corollary ,0103 physical sciences ,FOS: Mathematics ,010307 mathematical physics ,Ideal (ring theory) ,0101 mathematics ,Algebraic Geometry (math.AG) ,Mathematics - 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In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura.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
- Published
- 2021