Talk:Algebraic stack

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WikiProject Mathematics (Rated Start-class, Mid-importance)
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Mathematics rating:
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 Field: Geometry

The final sentence in the motivation section is broken. —Preceding unsigned comment added by (talk) 08:35, 2 February 2010 (UTC)

What even are these??? —Keenan Pepper 02:18, 16 November 2005 (UTC)

Proposing the article to be split[edit]

The article's title suggests that it covers stacks (i.e., fibred categories over a site (or a topos, or a topological space) for which "descent works"). However, the present article is essentially a stub for algebraic stacks, i.e., very particular types of stacks in groupoids that are suitably "covered" by algebraic spaces. Whereas stacks in general are a formalisation of a key concept in general descent theory, algberaic stacks (of the D-M and Artin types) are a generalisation of schemes. The two topics are in fact quite dissimilar in terms of questions considered and techniques used.

Thus, the article should be split into a new article on general stacks, and another one to cover algebraic stacks. For the general article a title like Stack (descent theory) would be better than Stack (category theory) as the framework for stacks includes also a Grothendieck topology and not only categories. Stca74 17:30, 3 September 2007 (UTC)

With no objections having emerged, I'm moving ahead with the split. I've requested speedy deletion of the redirect Algebraic stack to move this page there. I shall next establish the stub Stack (descent theory). Stca74 17:49, 9 September 2007 (UTC)
Split completed. We now have two stubs to work on — this one and Stack (descent theory). Stca74 05:56, 10 September 2007 (UTC)