Added "Pulling back sections" section in modules.tex#184
Open
eliasgv3 wants to merge 11 commits intostacks:masterfrom
Open
Added "Pulling back sections" section in modules.tex#184eliasgv3 wants to merge 11 commits intostacks:masterfrom
eliasgv3 wants to merge 11 commits intostacks:masterfrom
Conversation
- Moved everything from modules.tex to sheaves.tex. After all, the results we use are from the latter chapter, so it seemed to fit better there. - Defined the inverse image section, proven its functorial properties, and made the connection with the pullback section.
Member
|
I am going to leave this pull request open because it may make sense to add a little bit about this notion, but earlier and more naively. Namely, I would say that the compatibilities shown in this commit suggest that we've already been using this notion much earlier. And in fact, the construction in Section 21 of the pullback by f of a sheaf of sets F, as the sheafification of Related: variant for sheaves on sites and pullback on cohomology. |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Defined the pullback of a section of a sheaf of modules along a morphism of ringed spaces. Collected basic functorial properties.
I know this material may very basic, but it's nowhere treated. Despite this, the concept is extensively used in algebraic geometry and in particular in the Stacks Project:
f* : Γ_*(X,ℒ) → Γ_*(Y,f*ℒ).• The statement of Tag 08RU.
• The proof of Tag 0H79.
(The list might not be exhaustive, it's only the instances I came across so far.)