leanprover-community / leanprover-community/mathlib4
smooth morphisms of schemes and étale fundamental group
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t-algebra
t-algebraic-geometry
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- Lean
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Description
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 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
- #14271
- #14325
- #16727
- #16869
- #16853
- #16827
- #16868
- #19749
- #19748
- #21260
Smooth morphisms of schemes
- #17030
- #17028
- #17032
- #17264
- #17302
- #17305
- #17335
- #14161
Etale site
- #17734
- #17736
- #18727
- #18854
Etale fundamental group
- #22930
- #22918
- #22565
- #22339
- #22922
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reviewing the remaining checklist items and the referenced PRs, especially those under the Etale site and Etale fundamental group sections. Done means completing the outstanding theory tasks and updating this tracker with the relevant PRs.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 20/100