Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

[Merged by Bors] - feat(algebraic_geometry/structure_sheaf): Define comap on structure sheaf #7788

Closed
wants to merge 13 commits into from
Closed

[Merged by Bors] - feat(algebraic_geometry/structure_sheaf): Define comap on structure sheaf #7788

wants to merge 13 commits into from

Conversation

justus-springer
Copy link
Collaborator

@justus-springer justus-springer commented Jun 1, 2021 •
edited by jcommelin

@justus-springer justus-springer mentioned this pull request Jun 1, 2021
Closed
2 tasks
@github-actions github-actions bot added blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. merge-conflict Please `git merge origin/master` then a bot will remove this label. labels Jun 1, 2021
@github-actions github-actions bot removed the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Jun 2, 2021
@bryangingechen bryangingechen changed the title feat(algebraic_geoemtry/structure_sheaf): Define comap on structure sheaf feat(algebraic_geometry/structure_sheaf): Define comap on structure sheaf Jun 3, 2021
@github-actions github-actions bot added merge-conflict Please `git merge origin/master` then a bot will remove this label. and removed blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. labels Jun 9, 2021
@github-actions
Copy link

github-actions bot commented Jun 9, 2021

🎉 Great news! Looks like all the dependencies have been resolved:

💡 To add or remove a dependency please update this issue/PR description.

Brought to you by Dependent Issues (:robot: ). Happy coding!

@github-actions github-actions bot removed the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Jun 9, 2021
@justus-springer justus-springer added the awaiting-review The author would like community review of the PR label Jun 9, 2021
jcommelin
jcommelin reviewed Jun 9, 2021
View reviewed changes
Copy link
Member

@jcommelin jcommelin left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

How far are we from turning this into a morphism of sheaves?

src/algebraic_geometry/structure_sheaf.lean Outdated
If a section `s` on `U` is locally equal to the fraction `a/b`, its image on `V` is locally equal
to the fraction `f(a)/f(b)`.
-/
@[simps] def structure_sheaf.comap (f : R →+* S) (U : opens (prime_spectrum.Top R))
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Does @[simps] generate a useful _apply lemma here? The to_fun entry looks pretty intimidating.

Copy link
Collaborator Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Yes, it's used multiple times in the subsequent lemmas. The bulk of the to_fun entry is the proof that the section on V is again locally fraction, which doesn't show up in the _apply lemma any more. Still it's not exactly easy to read, I agree. I'm not sure how to improve it though. The comment above is meant to give an idea of what the definition means. Maybe I should expand upon that?

Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

One way to improve it might be to make an earlier definition comap_fun and use that here. That way you can govern to what extent simp will explode into a huge formula.

Copy link
Collaborator Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Okay, I will try to do that!

src/algebraic_geometry/structure_sheaf.lean Outdated Show resolved Hide resolved
src/algebraic_geometry/structure_sheaf.lean Outdated Show resolved Hide resolved
@justus-springer @jcommelin
Apply suggestions from code review
1be0a47 
Co-authored-by: Johan Commelin <johan@commelin.net>
@justus-springer
Copy link
Collaborator Author

justus-springer commented Jun 9, 2021 •
edited

How far are we from turning this into a morphism of sheaves?

It will be a morphism of sheaves in #7790. I didn't do it here because it requires Spec.Top_map, the comap on prime spectra, bundled as a morphism in Top. You need that to state the type of the sheaf morphism: structure_sheaf R ⟶ Spec.Top_map f _* (structure_sheaf S)

@jcommelin jcommelin self-assigned this Jun 9, 2021
@justus-springer justus-springer added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Jun 10, 2021
@justus-springer justus-springer added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Jun 11, 2021
@jcommelin
Copy link
Member

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-review The author would like community review of the PR labels Jun 11, 2021
bors bot pushed a commit that referenced this pull request Jun 11, 2021
@justus-springer
feat(algebraic_geometry/structure_sheaf): Define comap on structure s…
61a04c5 
…heaf (#7788)

Defines the comap of a ring homomorphism on the structure sheaves of the prime spectra.



Co-authored-by: justus-springer <50165510+justus-springer@users.noreply.github.com>
@bors
Copy link

bors bot commented Jun 12, 2021

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(algebraic_geometry/structure_sheaf): Define comap on structure sheaf [Merged by Bors] - feat(algebraic_geometry/structure_sheaf): Define comap on structure sheaf Jun 12, 2021
@bors bors bot closed this Jun 12, 2021
@bors bors bot deleted the structure_sheaf_comap branch June 12, 2021 02:37
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Reviewers

@jcommelin jcommelin jcommelin left review comments

Assignees

@jcommelin jcommelin

Labels
ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.)
Projects
None yet
Milestone
No milestone
Development

Successfully merging this pull request may close these issues.

None yet
2 participants
@justus-springer @jcommelin