Timeline for Do algebraic stacks satisfy fpqc descent?
Current License: CC BY-SA 3.0
12 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 27, 2015 at 15:14 | vote | accept | beginner | ||
| Mar 27, 2015 at 15:14 | comment | added | beginner | Thank you very much - this is exactly what I wanted (and I find it hard to see how an algebraic geometer could interpret the claim that "algebraic stacks with quasi-affine diagonal are fpqc sheaves" to mean that they are then forced to be sheaves in sets, but...). | |
| Mar 26, 2015 at 14:12 | comment | added | Denis Nardin | I see your point, but it is not clear to me that the question is using a different terminology than the answer. Anyway I don't think this is worth discussing further | |
| Mar 26, 2015 at 13:30 | comment | added | Niels | @Denis as I already mentioned in the first comment "algebraic stacks with quasi-affine diagonal are fpqc sheaves" is misleading since this can be understood as : a sheaf of sets. That is what most algebraic geometers will understand when you claim a stack is a sheaf. If the answer uses a different terminology than the question, there should be a warning. | |
| Mar 26, 2015 at 12:32 | comment | added | Denis Nardin | I guess my problem is that I don't understand how Adeel's answer can be misleading. In which sense could you misunderstand the sentence "algebraic stacks with quasi-affine diagonal are fpqc sheaves"? Also the fact that it referenced the stacks project does not mean that the person in question is interested mainly in algebraic geometry (even if I admit that's probably the case): homotopy theorists use algebraic stacks all the time! | |
| Mar 26, 2015 at 8:26 | comment | added | Niels | @Denis the question was formulated with a clear reference to the stacks project and to algebraic stacks, so I don't understand the point of your remark. | |
| Mar 25, 2015 at 13:33 | comment | added | Denis Nardin | @Niels This is, however, the standard terminology in homotopy theory (sometimes you see them referred as "homotopy sheaves" but the "homotopy" part is dropped more often than not). | |
| Mar 25, 2015 at 13:15 | comment | added | Niels | This is not the classical definition, for instance not the definition in the stacks project. What you call sheaf is simply misleading with the current terminology. | |
| Mar 25, 2015 at 9:33 | comment | added | AAK | @Niels, for me an algebraic stack is defined to be a sheaf of groupoids (satisfying some conditions), so I interpret the question as whether or not this sheaf satisfies fpqc descent. | |
| Mar 25, 2015 at 8:51 | comment | added | Niels | Both the question and your answer are ambiguous. Usually by sheaf one means sheaf of sets, whereas here you obviously mean fpqc "sheaf of groupoids", usually called fpqc stack. | |
| Mar 25, 2015 at 7:01 | history | answered | AAK | CC BY-SA 3.0 |