Smooth homomorphisms admit noetherian reductions
Commutative Algebra
2023-05-26 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2305.15409,
title = {Smooth homomorphisms admit noetherian reductions},
author = {Nitin Nitsure},
journal= {arXiv preprint arXiv:2305.15409},
year = {2023}
}
Comments
2 pages