Timeline for Some questions about the map $K_0(\text{Var})\to K_0(\text{Mot})$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 15, 2017 at 18:40 | comment | added | Mikhail Bondarko | Dear Marc, I have looked at your comment with suspicion for some time. Now I have realized that the arrows in your triangle should actually be reversed. Thus it makes sense to pass to (Verdier) duals to obtain the usual triangle of motives with compact support. | |
| Feb 15, 2017 at 7:53 | answer | added | Mikhail Bondarko | timeline score: 4 | |
| Feb 15, 2017 at 5:44 | answer | added | peterx | timeline score: 3 | |
| Feb 14, 2017 at 3:03 | comment | added | Marc Hoyois | If you replace $Mot$ by a suitable derived category of motives, then sending a variety to its Borel-Moore motive induces $K_0(Var) \to K_0(Mot)$ over any field. The point is that there is a triangle $M(Z) \to M(X) \to M(U)$. This works rationally always (all candidates for $Mot$ are equivalent then). Integrally it works with $Mot$ the category of $H\mathbb Z$-modules (the triangle is then essentially Bloch's localization theorem for higher Chow groups). | |
| Feb 13, 2017 at 22:38 | history | asked | peterx | CC BY-SA 3.0 |