leanprover-community / leanprover-community/mathlib4

smooth morphisms of schemes and étale fundamental group

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t-algebra t-algebraic-geometry
Dominant language
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

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. 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

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