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Results tagged with algebraic-stacks
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user 11682
6
votes
When quotient stacks (for nonsmooth group) are algebraic and related questions
About 1. : no, smoothness isn't essential.
"Flat is enough" : De Jong's slogan to express this result due to M.Artin.
https://www.math.columbia.edu/~dejong/wordpress/?p=1584
I quote :
"Given a flat, f …
- 4,008
6
votes
Do equivariant morphisms induce representable maps of quotient stacks?
Because
first, $Y\to [Y/G]$ is a chart
second, the following diagram
$$\require{AMScd}
\begin{CD}
X @>>> Y \\
@VVV @VVV \\
[X/G] @>>> [Y/G]
\end{CD}
$$
is cartesian (this is so because any morphis …
- 4,008
4
votes
Representability of morphism of stacks
This is http://stacks.math.columbia.edu/tag/04Y5 . I quote :
"
lemma
Let $S$ be a scheme contained in $Sch_{fppf}$.
Let $f : \mathcal{X} \to \mathcal{Y}$ be a $1$-morphism of algebraic
stacks over …
- 4,008
4
votes
Accepted
Group action on a stack and fixed points
A standard reference is
Romagny, Matthieu
Group actions on stacks and applications.
Michigan Math. J. 53 (2005), no. 1, 209–236.
http://projecteuclid.org/euclid.mmj/1114021093
http://perso.univ-re …
- 4,008
3
votes
Explicit description of the stack associated to a groupoid
This is called "Stackification via torsors" in the book by Kai Behrend, Brian Conrad, Dan Edidin, William Fulton, Barbara Fantechi, Lothar Göttsche and Andrew Kresch. See Andrew Kresch's homepage:
ht …
- 4,008