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Theory of smooth morphisms of schemes #16890

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chrisflav opened this issue Sep 17, 2024 · 0 comments

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t-algebra t-algebraic-geometry

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chrisflav commented Sep 17, 2024 •

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This issue is meant to track PRs on the development of the theory of smooth (and étale) morphisms.

The current rough layout is:

develop theory of standard smooth algebras and ring homomorphisms
define and show basic persistence properties of "locally standard smooth morphisms" of schemes
show that flat is a local property of ring homomorphisms
show that unramified is a local property of ring homomorphisms
show that smooth (i.e. formally smooth + fin. pres.) is equivalent to locally standard smooth
show that étale = flat + unramified

Open or already closed PRs on this topic:

Standard smooth algebras and ring homomorphisms

chrisflav added t-algebraic-geometry t-algebra labels

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