Timeline for Hypercohomology of a complex via Cech cohomology
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 8, 2013 at 13:42 | comment | added | Tom Bachmann | Indeed regarding "sufficiently nice": it suffices that for each $n$, the complex $C^{n, \bullet}$ computes the cohomology of $\scr{F}^n$ (consider the spectral sequence taking "vertical cohomology" first). | |
| Apr 8, 2013 at 12:14 | answer | added | Alicia Garcia-Raboso | timeline score: 5 | |
| Apr 8, 2013 at 9:42 | comment | added | ChrisLazda | I can't think of a reference, but I have a vague recollection that this is how you do it: since the Cech complex of a sheaf is functorial, if we have a complex of sheaves $\mathcal{F}^{\cdot}$ we can take the Cech complex of each term to get a double complex $C^{\cdot,\cdot}$. Now just take the associated simple complex, $\mathrm{Tot}(C^{\cdot,\cdot})$ - in suitably nice situations, this computes hypercohomology of $\mathcal{F}^{\cdot}$. | |
| Apr 8, 2013 at 6:50 | history | asked | none | CC BY-SA 3.0 |