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[Merged by Bors] - feat(ring_theory/algebra_tower): Artin--Tate lemma #4282

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[Merged by Bors] - feat(ring_theory/algebra_tower): Artin--Tate lemma #4282

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kckennylau
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sgouezel
sgouezel reviewed Sep 27, 2020
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src/ring_theory/algebra_tower.lean Outdated
(λ p q _ _ hp hq, hyy $ submodule.mul_mem_mul hp hq)
end

/- Artin--Tate lemma. Atiyah--Macdonald Proposition 7.8; Stacks 00IS; Altman--Kleiman 16.17. -/
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/-- instead of /-? Also, can you explain in the docstring the mathematical content of the theorem, with words?

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Done.

jcommelin
jcommelin requested changes Sep 28, 2020
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I think this looks great. Thanks a lot for doing this.

src/ring_theory/adjoin.lean
theorem fg_def {S : subalgebra R A} : S.fg ↔ ∃ t : set A, set.finite t ∧ algebra.adjoin R t = S :=
⟨λ ⟨t, ht⟩, ⟨↑t, set.finite_mem_finset t, ht⟩,
λ ⟨t, ht1, ht2⟩, ⟨ht1.to_finset, by rwa set.finite.coe_to_finset⟩⟩

theorem fg_bot : (⊥ : subalgebra R A).fg :=
⟨∅, algebra.adjoin_empty R A⟩

lemma fg_of_submodule_fg (h : (⊤ : submodule R A).fg) : (⊤ : subalgebra R A).fg :=
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Do we want (⊤ : submodule R A).fg) and (⊤ : subalgebra R A).fg to be the idomatic way of saying module.finite R A and algebra.finite R A? I think I wouldn't mind having those definitions. It looks better, and potentially, those should be classes...

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maybe in a separate PR.

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Thanks 🎉

bors merge

Ok, let's merge this... but I would really like to see that separate PR. 😺

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Sep 28, 2020
bors bot pushed a commit that referenced this pull request Sep 28, 2020
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feat(ring_theory/algebra_tower): Artin--Tate lemma (#4282)
d437393
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bors bot commented Sep 28, 2020

Build failed (retrying...):

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bors r-

CI is failing

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bors bot commented Sep 28, 2020

Canceled.

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Let's try again

bors r+

bors bot pushed a commit that referenced this pull request Sep 28, 2020
@kckennylau
feat(ring_theory/algebra_tower): Artin--Tate lemma (#4282)
60ee385
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bors bot commented Sep 28, 2020

Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Sep 28, 2020
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feat(ring_theory/algebra_tower): Artin--Tate lemma (#4282)
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Build failed:

@robertylewis robertylewis added awaiting-author A reviewer has asked the author a question or requested changes and removed ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) labels Sep 28, 2020
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@kckennylau Could you please take a look at what is wrong?

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jcommelin approved these changes Sep 29, 2020
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Thanks 🎉

bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-author A reviewer has asked the author a question or requested changes labels Sep 29, 2020
bors bot pushed a commit that referenced this pull request Sep 29, 2020
@kckennylau @robertylewis
feat(ring_theory/algebra_tower): Artin--Tate lemma (#4282)
0bb5e5d 
Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com>
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bors bot commented Sep 29, 2020

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(ring_theory/algebra_tower): Artin--Tate lemma [Merged by Bors] - feat(ring_theory/algebra_tower): Artin--Tate lemma Sep 29, 2020
@bors bors bot closed this Sep 29, 2020
@bors bors bot deleted the artin-tate branch September 29, 2020 06:26
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@jcommelin jcommelin jcommelin approved these changes

@ChrisHughes24 ChrisHughes24 Awaiting requested review from ChrisHughes24

@kbuzzard kbuzzard Awaiting requested review from kbuzzard

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