Year: 2023
Type: preprint
Abstract: We give a short proof that any smooth (means formally smooth and finitely presented) homomorphism of rings can be obtained by base change from a smooth homomorphism of noetherian rings. Together with the elegant short proof by J. Conde-Lago that smooth homomorphisms of noetherian rings are flat, this gives a short and elementary proof of the theorem of Grothendieck that all smooth homomorphisms are flat.
Source: arXiv (Cornell University)
Author: Nitsure, Nitin
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4378498602