All Questions
8 questions with no upvoted or accepted answers
8
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325
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Moduli stacks and representability of diagonal by schemes
The answer to my question might very well be standard, but I have had trouble finding the right keywords to search for it, so I apologize if this is something well-known to the experts.
I am learning ...
- 28.2k
6
votes
0
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254
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Is the stack of varieties with a big line bundle algebraic
In Starr's paper https://www.math.stonybrook.edu/~jstarr/papers/moduli4.pdf the folk result that the fibred category of pairs $(X\to S, L)$, where $S$ is an affine scheme, $X\to S$ is flat proper ...
- 171
3
votes
0
answers
291
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Generalizations of Artin–Verdier duality?
Constructible étale abelian sheafs on $Spec\ O_\mathbb K$, for number fields $\mathbb K$, satisfy Artin-Verdier duality. Are there known any algebraic schemes or algebraic stacks, other than $Spec\ O_\...
- 2,390
3
votes
0
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303
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Finiteness of the connected components of a stack
Let $X$ be an algebaic stack over a scheme $S$, for any $S$-scheme $Y$ we can consider the groupoid $X(Y)$ of $Y$-points. Denote by $\pi_0(X(Y))$ the set of isomorphism classes of the groupoid.
Are ...
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3
votes
0
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410
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Quasi-finite morphisms of stacks
Let $f:X\to Y$ be a morphism of ``nice" stacks over $\mathbf C$ such that the induced morphism on coarse moduli spaces is quasi-finite. Is $f$ quasi-finite?
By a "nice" stack I mean a smooth finite ...
- 31
2
votes
0
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139
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What are the categories of IND and PRO schemes?
below is a mathexchange question with no answers so I drop it here.
I have some difficulties to figure out what the category of IND-schemes and PRO-schemes are, in particualer the relations with ...
- 1,270
2
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0
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127
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$\mathscr Coh_{X|S} $ is algebraic and of finite type
Let $S$ be a Noetherian scheme and $X$ a projective $S$-scheme.
Reading Laumon-Moret--Bailly's "Champs Algebriques", Theorem 4.6.2.1:
$ \mathscr Coh_{X|S} $ and $ \mathscr Fib_{X|S,r} $ are ...
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1
vote
0
answers
263
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An algebraic stack is an algebraic space if and only if it has the trivial stabilizer group
Let $G\to S$ be a smooth affine group scheme over a scheme. Let $U$ be a scheme over $S$ with an action of $G$. Let $[U/G]$ be the quotient stack.
In Alper's note: Stacks and Moduli, there is a result ...
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