Timeline for What exactly does it mean for the moduli space of stable sheaves to have a universal family étale locally?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 24 at 23:43 | comment | added | quasicoherent_drunk | @PiotrAchinger I see, thank you! | |
| Nov 22 at 8:56 | comment | added | Piotr Achinger | The local maps $X\to U$ need not be unique (otherwise they would glue to a global map $X\to U$, and then $U\to\mathcal{M}$ would be an isomorphism). | |
| Nov 22 at 8:55 | comment | added | Piotr Achinger | I think it means that the moduli stack $\mathcal{M}$ (the "functor" associating to every $S$ the groupoid of suitable stable sheaves on $S\times X$) admits an etale surjection from a scheme $U$. That is, a natural transformation ${\rm Hom}(-, U)\to \mathcal{M}$ (corresponding by Yoneda to a suitable family of stable sheaves parametrized by $U$) such that every map $X\to \mathcal{M}$ etale locally on $X$ lifts to $U$. This means that every family parametrized by $X$ is etale locally on $X$ the pullback of the family on $U$ via some map. The map to the coarse moduli space $M$ need not be etale. | |
| S Nov 22 at 4:33 | review | First questions | |||
| Nov 22 at 5:08 | |||||
| S Nov 22 at 4:33 | history | asked | quasicoherent_drunk | CC BY-SA 4.0 |