All Questions
Tagged with algebraic-spaces representable-functors
7 questions
2
votes
0
answers
175
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Is this double quotient of $\operatorname{SL}_2$ representable by an algebraic space or a scheme?
$\DeclareMathOperator\SL{SL}$Let $B$ be a Borel subgroup (upper triangular matrices), and let $\Gamma := \langle \sigma\rangle$ be the group generated by a (hyperbolic) element of $\SL_2/\mathbb{Q}_p$ ...
- 2,907
8
votes
0
answers
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
5
votes
0
answers
283
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Reference for Grothendieck's theorem on representation of unramified functors
In the Exposé 294 of the Bourbaki Seminar of the year 1964-1965, Murre gives an outline of proof of a theorem of Grothendieck giving necessary and sufficient conditions of representability by a scheme ...
- 4,482
0
votes
1
answer
87
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representing base changes of the unit section
Let $S$ be a scheme and $G$ be a sheaf in groups on the big étale site over $S$. Let $e:S\rightarrow G$ be the unit section. Is it true that given an algebraic space in groups $H$, étale over $S$, and ...
- 13
7
votes
2
answers
800
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Is an algebraic space over a DVR, whose special fibre and generic fibre are schemes, actually a scheme?
Is an algebraic space over a DVR, whose special fibre (and all its infinitesimal neighborhood) and generic fibre are schemes, actually a scheme?
- 997
0
votes
1
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226
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Prorepresentable functors repres. by alg. spaces? Covering spaces by alg. spaces.
Let $X$ be a (reasonable) scheme. I'm curious about constructing the constructing the covering space of a scheme algebraically. The covering space functor $F$ (below) can be represented by a ...
- 3,555
6
votes
2
answers
789
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Do quotients of representable sheaves represent quotients?
Here's the context for the question: Proposition 4.6 of Freitag and Kiehl's book on etale cohomology shows that a sheaf (of sets) $\mathcal{F}$ (on the site Et(X)) is constructible if and only if it ...
- 1,988