A DESCENT THEOREM FOR FORMAL SMOOTHNESS

A DESCENT THEOREM FOR FORMAL SMOOTHNESS

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 r...

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Veröffentlicht in:Nagoya mathematical journal 2018-03, Vol.229, p.113-140
1. Verfasser: MAJADAS, JAVIER
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Descent
Homology
Homomorphisms
Intersections
Set theory
Smoothness
Theorems
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Zusammenfassung: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.
ISSN:0027-7630
2152-6842
DOI:10.1017/nmj.2016.64