Two questions on algebraic stacks - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T12:38:35Z http://mathoverflow.net/feeds/question/48196 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48196/two-questions-on-algebraic-stacks Two questions on algebraic stacks Daniel Larsson 2010-12-03T17:16:47Z 2010-12-03T18:53:38Z <p>Question 1: The main reference on algebraic stacks (Laumon and Moret--Bailly) defines a separable algebraic stack as one having universally closed diagonal. For schemes separability is simply defined by the condition that the diagonal is a closed immersion. Why this difference?</p> <p>Question 2: Presentations of algebraic stacks are defined (in LMB) as morphisms (with some properties) $X\to\mathscr{X}$ with $X$ an algebraic space. What does one lose by only considering schemes $X$ instead?</p> <p>These questions are certainly well-known to experts in stack theory and I know there are a few around on MO, so I'm hopeful that I will be sufficiently enlightened.</p>