Timeline for Descent of sheaves under galois covering
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2016 at 18:21 | comment | added | abx | I think the statement in Huybrechts-Lehn is slightly incorrect: one should assume that the subsheaf $\mathcal{G}$ of $\pi ^*\mathcal{F}$ is saturated, that is, the quotient $\pi ^*\mathcal{F}/\mathcal{G}$ is torsion-free. A maximum destabilizing subsheaf has this property, so their proof still works. You want to prove that the natural homomorphism $\pi ^*((\pi _*\mathcal{G})^G)\rightarrow \mathcal{G}$ is an isomorphism in codimension 1. I think this follows by considering the exact sequence $0\rightarrow \mathcal{G}\rightarrow \pi ^*\mathcal{F}\rightarrow \mathcal{Q}\rightarrow 0$. | |
| Jan 10, 2016 at 3:56 | comment | added | Diego Maradona | Could you show me how to prove an invariant subsheaf of $\pi^*F$ can be descent? | |
| Jan 9, 2016 at 15:45 | history | answered | abx | CC BY-SA 3.0 |