Timeline for Bousfield Lattices for which Minimal Objects Coproduct to Sphere Object
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2012 at 18:22 | comment | added | Jonathan Beardsley | Thanks for all the help @Greg and @Fernando. Checking out that Neeman paper now! | |
| Sep 5, 2012 at 10:09 | comment | added | Greg Stevenson | It is true for the unbounded derived category of a noetherian ring: the minimal Bousfield classes (which are not all of $D(R)$) are $\langle k(\mathfrak{p})\rangle$ and $$0 = \langle \coprod_{\mathfrak{p}} k(\mathfrak{p}) \rangle$$ as tensoring with the residue fields detects whether an object is non-zero. I am fairly sure it is not known what conditions would suffice in general; as Fernando points out this is probably a difficult issue. | |
| Sep 5, 2012 at 8:46 | comment | added | Fernando Muro | Probably you know MR1174255 Neeman, Amnon The chromatic tower for D(R). With an appendix by Marcel Bökstedt. Topology 31 (1992), no. 3, 519–532. | |
| Sep 4, 2012 at 23:31 | comment | added | Jonathan Beardsley | Yeah. I'm especially wondering if this is the case for the derived category of a Noetherian ring. I'll have to do some more reading on it. | |
| Sep 4, 2012 at 22:14 | comment | added | Fernando Muro | I think that computing the Bousfield lattice of an arbitrary stable homotopy category is a huge problem, so you can probably find explicit examples satisfying your conditions, e.g. among derived categories of commutative noetherian rings, but general conditions... that looks like very complicated. | |
| Sep 4, 2012 at 20:03 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |