A DESCENT THEOREM FOR FORMAL SMOOTHNESS. (8th December 2016)

• Record Type: Journal Article
• Authors: MAJADAS, JAVIER
• Is Part Of: Nagoya mathematical journal. Volume 229(2018)
• Page Start: 113
• Page End: 140
• Publication Date: 2016-12-08
• Subjects: 14B25, -- 13F40, -- 14B10; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1017/nmj.2016.64
• Languages: English
• ISSNs: 0027-7630

Abstract

Abstract : We give a descent result for formal smoothness having interesting applications: we deduce that quasiexcellence descends along flat local homomorphisms of finite type, we greatly improve Kunz's characterization of regular local rings by means of the Frobenius homomorphisms as well as André and Radu relativization of this result, etc. In the second part of the paper, we study a similar question for the complete intersection property instead of formal smoothness, giving also some applications.