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Let $\pi:X\to\mathcal X$ be a presentation of an Artin stack $\mathcal X$ of finite type over a field $k,$ and let $f:Y\to X$ be a finite \'etale covering. Does there exist a finite \'etale covering $ …

A stack (or a morphism of stacks, not necessarily representable) is defined to be smooth if one can find a presentation which is smooth over the base. …

The question depends on which maps you want to call "etale". If one thinks that the property of $f:X \to Y$ being etale should be etale local on $X,$ then etale morphisms doesn't need to be representa …

One can first define a 'proper algebraic space' $X,$ using its 'underlying space' $|X|,$ and then define a morphism of algebraic spaces $f: X \to Y$ to be proper if for any affine (or just quasi-compa …

I'm looking for references on constructible sheaves and the six operation formalism on analytic stacks (stacks fibered over complex analytic spaces). Does anyone have some suggestions? … Basically I want it to be an analytic version of Laszlo and Olsson's articles "The six operations for sheaves on Artin stacks, I, II", or a stack version of Dimca's book "Sheaves in Topology". …

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 is the diagonal neces …

My question is, is this true for stacks? Namely if $Y \to X$ is a representable finite etale map of algebraic stacks, can it be refined to a representable Galois morphism $Z \to X?$ …

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 coarse moduli space is that it has finite inertia stack. …

This is roughly what I know about how to do devissage on algebraic stacks. It may or may not apply to differentiable stacks. …

Hello Ben, a little comment: when you say "G is a group scheme over k", you mean k is a separably closed field, right? Because otherwise the groupoid BG(k) may not have only one isomorphism class of …

Algebraic spaces are non-stacky algebraic (Artin) stacks, and DM-stacks, although stacky, have only finite stabilizer groups (or étale stab. groups; I'm sloppy here) for all points on the "underlying space … stacks, lisse-étale topology is necessary. …