A couple weeks ago I attended a talk about the Keel-Mori theorem regarding existence of coarse moduli spaces for Deligne-Mumford stacks with finite inertia. Here are some questions …

The title is vague, my actuall question is the following: Has the representations of groupoids been systematically studied? Is there any new phenomenon, compare with the represent …

This is probably pretty basic, but as I said before I'm just beginning my way in the language of stacks.Say you have an etale cover X->Y of stacks (in the etale site). Is there a s …

Background/motivation One of the main reason to introduce (algebraic) stacks is build "fine moduli spaces" for functors which, strictly speaking, are not representable. The yoga i …

Artin has a theorem (10.1 in Laumon, Moret-Bailly) that if $X$ is a stack which has separated, quasi-compact, representable diagonal and an fppf cover by a scheme, then $X$ is alge …

I'm a bit confused by the double role which sheaves play in the theory of stacks. On the one hand, sheaves on a site are the obvious generalization of a sheaf on a topological spa …

I'm taking my first steps in the language of stacks, and would like something cleared up. The intuitive idea of moduli spaces is that each point corresponds to an object of what we …

Let $B$ be a ring which is the colimit of rings $B_\lambda$. Let $X_\lambda$ be a stack (not necessarily algebraic) over $B_\lambda$ such that $X_\lambda \times_{B_\lambda} B_\mu …

Are there any good introductory texts on algebraic stacks? I have found some readable half-finsished texts on the net, but the authors always seem to give up before they are finish …

So, let's say one has an action of $GL_n$ on an algebraic variety $X$ over a field $k$, and two objects $F,G$ in the equivariant derived category (i.e., the derived category of con …

This is related to another one of my questions on DM stacks. In Brian Conrad's article 'The Keel-Mori Theorem via Stacks', a sufficient condition on for an Artin stack to have coar …

I have seen the use of the word "proper Deligne-Mumford stack". Now, it is clear to me what it means for a morphism f of stacks to be proper: as usual it should be representable, a …

A scheme is separated if the diagonal inclusion $X \to X \times X$ is a closed immersion. I what to know if there is a good generalization of `separated' for algebraic stacks? My …

Let X be a DM stack over a field k. We follow the definition in Laumon and Moret-Bailly's book, so that its diagonal is quasi-compact (and hence diagonal is of finite type). Then i …

Let $X$ be a smooth projective algebraic variety over $\mathbb{C}$. Then I think that someone (Serre?) showed that the Cohomological Etale Brauer Group agrees with the torsion par …