Timeline for Cosheaf homology and a theorem of Beilinson (in a paper on Mixed Tate Motives)
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 3, 2019 at 10:46 | comment | added | David Corwin | Looking back at this, the main problem I had with the D-G proof was that I did not understand (co)simplicial objects very well then. | |
| Apr 10, 2018 at 6:48 | answer | added | მამუკა ჯიბლაძე | timeline score: 3 | |
| Jan 20, 2013 at 0:40 | answer | added | Justin Curry | timeline score: 15 | |
| Jul 26, 2012 at 1:03 | comment | added | David Corwin | Thanks, I had seen that proof, but I found it to be unnecessarily non-elementary. | |
| Jul 25, 2012 at 19:09 | comment | added | AFK | You can also rewrite the proof quite easily if you remember that (1) Goncharov's objective is to compute $H_n(P^n_{x,y}X,\partial P^n_{x,y} X)$ ($P^n_{x,y}X=\{x\}\times X^n \times \{y\}$ the cosimplicial path space) (2) In the formalism of 4 operations $$H_n(X,Z;A) = {}^\tau H^{−n}(a_{X!} j_{∗} j_{∗} a^{!}_X A)$$ with $\tau$ is the t-structure, $a_X:X\to pt$ the structural morphism, $j:X\setminus Z \hookrightarrow Z$ is the open immersion. (3) The proof in Deligne-Goncharov is Poincaré dual in the sense that they compute $$ H^n(X \mod Z;A) = {}^{\tau} H^n( a_{X } j! j^! a_X^{} A ) $$ | |
| Jul 25, 2012 at 19:02 | comment | added | AFK | The proof was rewritten in the framework of sheaf cohomology in Deligne and Goncharov's "Groupe fondamentaux motiviques de Tate mixtes". This is french but should still be easier to understand. | |
| Jun 21, 2012 at 13:50 | comment | added | S. Carnahan♦ | Wild guess for (4): Given a subvariety, you may push the constant cosheaf on that subvariety forward along the inclusion map, and take the derived functors. | |
| Jun 19, 2012 at 4:07 | history | asked | David Corwin | CC BY-SA 3.0 |