2023/03/23 by Nitsure, Nitin
#13B40 #14B25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.15409
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.