Timeline for What would cohomological localization be good for?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Oct 18, 2022 at 4:03 | history | bounty ended | CommunityBot | ||
| S Oct 18, 2022 at 4:03 | history | notice removed | CommunityBot | ||
| Oct 10, 2022 at 13:26 | answer | added | D.-C. Cisinski | timeline score: 2 | |
| S Oct 10, 2022 at 2:48 | history | bounty started | Noah Schweber | ||
| S Oct 10, 2022 at 2:48 | history | notice added | Noah Schweber | Draw attention | |
| Sep 1, 2019 at 9:09 | comment | added | Neil Strickland | The point is just that for many spectra $A$, one can produce a spectrum $B$ such that cohomological localisation with respect to $A$ is the same as homological localisation with respect to $B$. Examples are given in Hovey's paper "Cohomological Bousfield classes". There are many applications for cohomological localisation, but it just turns out that all the examples that have been needed agree with homological localisations. | |
| Sep 1, 2019 at 0:11 | comment | added | Mike Shulman | @NeilStrickland Interesting. Can you give any explanation for why the difference in applications between homological and cohomological localization? For instance, many of the answers to mathoverflow.net/q/173546/49 would apply equally to cohomological localization. | |
| Aug 31, 2019 at 23:38 | comment | added | Neil Strickland | I am not aware of any specific applications of cohomological localisations, except in cases where they can be proven to be the same as homological localisations; things would just be tidier if we knew that they existed. | |
| Aug 31, 2019 at 13:20 | history | asked | Mike Shulman | CC BY-SA 4.0 |