Daniel Bergh
  • Member for 12 years, 2 months
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Is an algebraic space group always a scheme?
8 votes

Over a general base the answer is no, as pointed out to me by Matthieu Romagny in response to this question. He gives a reference to Lemma X.14 of Raynaud's book "Faisceaux amples sur les schémas en ...

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coarse moduli space and $\pi_0$
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7 votes

You have probably already come up with the answer yourself, but I just thought the question shouldn't hang around unanswered in the forum. What you call "the sheaf of connected components", I would ...

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Stabilizer Action on vector bundle on a stack
6 votes

For the first question the short answer is that the map $x$ factorises canonically through the classifying stack $BG$ with $G = Stab(x)$ and the category of quasi-coherent modules on $BG$ is ...

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Non-cohomological proof that the pullback of an ample bundle by a finite morphism is ample
4 votes

This has nothinging to do with finiteness. Let $f:X\to Y$ be affine and $L$ a line bundle on $Y$. Then the subschemes $Y_s$ for $s \in \Gamma(Y, L^n)$ pull back to subschemes $X_{f^*s}$. Hence $L$ is ...

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Pulling back the lisse-etale structure sheaf via the inclusion of a point
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3 votes

EDIT I just realized that my previous version of the answer was totally misleading. Here is what really is problematic in your argument: Just because the images of $t$ and $t^2$ are distinct in $\...

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Sequences of groups, exact not just in étale but also in the Zariski topology
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3 votes

Let me elaborate on Torstens comment. The map $GL_n(B) \to i_*F$ in your example is an fppf $D^\times$-torsor over $i_*F$, a fact which can be checked easily directly from the definition of torsor ...

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Irreducibility of quotient stacks.
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3 votes

If you have a presentation $s, t:R \to U$ of a stack $[U/R]$, the set of points of $[U/R]$ is just the equivalence classes of points in $|U|$ determined by the equivalence relation given by the image ...

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Does this condition reduce to the correct notion of irreducibility on schemes?
2 votes

Yes, it is the same concept since the fibre products of schemes DO coincide with the fibre product of the underlying topological spaces in the case of open immersions (Check, for instance, Hartshornes ...

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Why do we need finiteness conditions for formally étale morphisms?
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2 votes

I guess, to get a good theory, you would want to be able to have effective descent for certain classes maps. In Brian Conrads answer to this question: "Quasi-separatedness for Algebraic Spaces" he ...

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An alternative definition of pseudo-coherent complex
1 votes

Yes, provided that $X$ is a scheme (or, for instance, an algebraic stack). In particular, we need not assume that $X$ is locally noetherian. Let $(X, \mathcal{O}_X)$ be a locally ringed space (or a ...

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Precise definition of a scheme (Key question: How to define an open subfunctor without resorting to classical scheme theory)
1 votes

I'm not sure if this is what you are after, but when I started to look at Grothendieck-topologies I thought of being an open immersion as a topological property; somehow it should be possible to ...

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