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arXiv · 2305.15409

Smooth homomorphisms admit noetherian reductions

Nitin Nitsure
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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.

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Nitin Nitsure. 2023-03-23. Smooth homomorphisms admit noetherian reductions. https://arxiv.org/abs/2305.15409

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