Timeline for Spectra with "finite" homology and homotopy
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2018 at 8:25 | comment | added | Q. Q. | @skd, I mean, consider the category of all spectra (not p-complete), denote by I the Brown-Comenetz dual of sphere spectrum (not p-version of it). Why X^I = 0 if and only if F(X, S) is contractible? | |
| Nov 6, 2018 at 22:44 | comment | added | skd | @ShayBenMoshe yes, you're right. | |
| Nov 6, 2018 at 20:59 | comment | added | Shay Ben Moshe | @skd, just a small remark, unless I missed something, I think you need simply connected for McGibbon-Neisendorfer, otherwise $S^1$ is a counter example. | |
| Nov 6, 2018 at 17:15 | comment | added | skd | What do you mean by "such generality"? You don't need X to be finite to conclude that X smash I = 0 if and only if F(X, S^0) = 0. | |
| Nov 6, 2018 at 7:08 | comment | added | Q. Q. | Yes, I mean F(I,I) = S^0 but can not edit now. I am also interested in this statement for all spectra and now wondering if it is true in such generality? It seems to agree on HZ: HZ^I=0 and F(HZ,S^0)=0. | |
| Nov 5, 2018 at 19:13 | history | edited | skd | CC BY-SA 4.0 |
added 32 characters in body
|
| Nov 5, 2018 at 19:12 | comment | added | skd | I'd implicitly p-localized. Note that since the difference you are after disappears after rationalization, it suffices to even work in the p-complete stable category to observe this distinction. Also, F(I,I) is not equivalent to I. | |
| Nov 5, 2018 at 19:08 | comment | added | Q. Q. | Thanks a lot for this answer, but i don't understand some things. "Strickland argues that if X is a spectrum, then X is IQ/Z-acyclic if and only if F(X,S0) is contractible." I understand his arguments for prime p, but I don't understand how to deduce the full statement. In his argument is critical that F(I,I) = I, which is not true for genuine Brown-Comenetz. | |
| Nov 5, 2018 at 3:24 | history | edited | skd | CC BY-SA 4.0 |
Maclane --> MacLane
|
| Nov 5, 2018 at 3:13 | history | answered | skd | CC BY-SA 4.0 |