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Apr 29, 2020 at 15:33 answer added Praphulla Koushik timeline score: 1
Apr 29, 2020 at 12:02 history edited Conjecture CC BY-SA 4.0
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Apr 29, 2020 at 11:34 comment added Daniel Loughran 2. and 3. are genuinely different in general. Just take $f: \mathcal{X} \to \mathrm{Spec} k$ an algebraic space over a field $k$ which is not a scheme. Then this is representable in the sense of 2., but not 3. For stacks definition 2. is the right one in general; sometimes authors refer to 3. as "strongly representable" or "schematic" to differentiate.
Apr 29, 2020 at 11:04 history asked Conjecture CC BY-SA 4.0