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Theory of smooth morphisms of schemes #16890

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2 of 7 tasks
chrisflav opened this issue Sep 17, 2024 · 0 comments
Open
2 of 7 tasks

Theory of smooth morphisms of schemes #16890

chrisflav opened this issue Sep 17, 2024 · 0 comments
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t-algebra Algebra (groups, rings, fields, etc) t-algebraic-geometry Algebraic geometry

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@chrisflav
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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 smooth morphisms of schemes
  • define the étale site
  • 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

Smooth morphisms of schemes

Etale site
@chrisflav chrisflav added t-algebraic-geometry Algebraic geometry t-algebra Algebra (groups, rings, fields, etc) labels Sep 17, 2024
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