Talk:Stack (mathematics)

Requested move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: Moved without dissent. Nathan Johnson (talk) 17:39, 29 May 2013 (UTC)

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Stack (descent theory) → Stack (mathematicis) – Very misleading/POV article title. A "stack" is a sort of generalization of a sheaf; it doesn't have to be limited to the descent theory. Taku (talk) 20:54, 21 May 2013 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Fixing some links to this page

I moved the title with the typo, Stack (mathematicis) (ending in "-cis") to Stack (mathematics).

The reason for moving this away from Stack (descent theory) was good but childishly naive. It didn't seem to occur to the person proposing this that the lay reader seeing "descent theory" would probably think it's about genealogy, or otherwise fail to realize it's about mathematics. Things like that should be borne in mind when choosing article titles! If Wikipedia were supposed to be simply an encyclopedia of mathematics, that would be another story.

But now we have this problem: Some pages link to Stack (descent theory). Linking through a redirect is not always really a problem, but in this case the present title seems clearly preferable. I've fixed _some_ of those links. Can others help with that too? Michael Hardy (talk) 18:53, 30 May 2013 (UTC)

Changed the remaining links in _articles_only_. --Cspan64 (talk) 21:41, 1 August 2013 (UTC)

What does "stacky" mean?

The adjective "stacky" is used at e.g. Toric stack; can it be defined here please? Equinox (talk) 13:56, 22 August 2015 (UTC)

I don't think it has any technically specific meaning; but it usually means "related to stacks". For another example, see Behrend's trace formula, which talks about the "stacky way" of counting objects (namely don't ignore automorphisms). -- Taku (talk) 20:47, 26 August 2015 (UTC)

Wrong example

I think the example of a stack that is not a global quotient is wrong. The constant group scheme Z/2 x S_3 acts on both Z/2 and S_3 (both also constant group schemes, say we are over a field) in the natural way. The quotient stack [S_3 \cup Z/2 / Z/2 x S_3] is exactly B Z/2 \cup B S_3. — Preceding unsigned comment added by 207.244.140.86 (talk) 21:10, 27 August 2017 (UTC)

You are correct! Thanks for pointing this out. Username6330 (talk) 08:02, 29 September 2017 (UTC)

Todo

• Mention isomorphism between $\mathbb {P} (2,3)$ and the moduli space of elliptic curves.
• Discuss examples of sheaves. Start with line bundles over weighted projective spaces and show they behave just like in the projective case.
• Explain sheaf cohomology computations on stacks
• Discuss types of morphisms of stacks similar to schemes (e.g. quasicompact, flat, etc.)

Several unclear terms in the intro

Quoting from the introduction:

Descent theory is concerned with generalisations of situations where isomorphic, compatible geometrical objects (such as vector bundles on topological spaces) can be "glued together" within a restriction of the topological basis.

What does "within a restriction of the topological basis" mean?

In a more general set-up the restrictions are replaced with pullbacks;

I believe it is unclear what rôle is played by pullbacks here.

Mamuka Jibladze (talk) 12:11, 3 August 2021 (UTC)