Timeline for Quasi-separatedness for Algebraic Spaces
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2010 at 14:12 | history | edited | BCnrd | CC BY-SA 2.5 |
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| Feb 26, 2010 at 17:18 | vote | accept | Daniel Bergh | ||
| Feb 26, 2010 at 17:18 | comment | added | Daniel Bergh | Then I think it starts to clear up a bit. Thanks a lot! | |
| Feb 26, 2010 at 16:06 | comment | added | BCnrd | Yes, provided that in 3 it is understood that the map U --> X is required to be representable (so "etale" makes sense for it). If you drop condition 2 then as a matter of good writing one ought to make the hypothesis of representability of U --> X in 3 more explicit in the statement (before saying it is "etale"). | |
| Feb 26, 2010 at 11:55 | comment | added | Daniel Bergh | Ok, do I get you right if I'm interpreting what you are saying as follows: A) Given any étale equivalence relation $R \subset U \times U$ of schemes, the étale sheaf quotient satisfies 1 - 3. (3 by [RG, I, 5.7.2] as referenced in your paper and 2 by your Proposition A.1.1) B) 1), 3) implies 2) in Chris' definition. (We may construct an étale equivalence relation from 1 and 3, so 2 follows from A). | |
| Feb 26, 2010 at 8:28 | history | edited | BCnrd | CC BY-SA 2.5 |
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| Feb 26, 2010 at 7:08 | history | answered | BCnrd | CC BY-SA 2.5 |