Timeline for Deformation of "Hecke modification"
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14, 2018 at 2:54 | vote | accept | La folia | ||
| Mar 7, 2018 at 6:40 | comment | added | Sasha | @Lafolia: I added some details to the answer. | |
| Mar 7, 2018 at 6:39 | history | edited | Sasha | CC BY-SA 3.0 |
added 501 characters in body
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| Mar 7, 2018 at 0:07 | comment | added | La folia | @Sasha: Could you explain where does this long exact sequence come from? | |
| Mar 6, 2018 at 16:58 | comment | added | Will Sawin | You can also represent this as the sheaf hypercohomology of the complex $\mathcal{H}om(E,E) \oplus \mathcal{H}om(F,F) \to \mathcal{H}om (F,E)$. The cohomology of this complex in the category of sheaves can be computed explictly as, in degree zero, a length one modification of $\mathcal{H}om (E,E)$ and, in degree one, a rank one skyscraper sheaf at $x$. The contribution of this skyscraper sheaf to the cohomology should be the map to $T_x X$. | |
| Mar 5, 2018 at 21:01 | comment | added | S. carmeli | This is very nice! I just want to comment on how this answer is equivalent to my answer below (and I give up the claim that it is not classical homological algebra of course!), the map into the sum of ext's being forgetting the chosen homotopy and the $Hom(F,E)$ component the fiber of this forgetting map. The conditions on the image in the $Ext^1$-terms come from the commutativity constrain, and the quotient on the term on the right from the effect of re-choosing $d_{\tilde{F}}$ and $d_\tilde{E}$ within a homotopy class on the choice of homotopy. | |
| Mar 5, 2018 at 20:35 | history | answered | Sasha | CC BY-SA 3.0 |