Timeline for K-theory and K-theory pushforward in topology vs. in algebraic geometry
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Oct 12, 2011 at 1:12 | answer | added | Kevin H. Lin | timeline score: 5 | |
| Oct 12, 2011 at 1:07 | comment | added | Kevin H. Lin | @Anatoly, thanks for the elaboration! That's interesting, and helpful. | |
| Oct 12, 2011 at 0:57 | comment | added | Tom Goodwillie | It's false already for elliptic curves. | |
| Oct 12, 2011 at 0:55 | comment | added | Anatoly Preygel | And Remark 4.17 of op.cit., and the text around it, discusses the compatibility of that relationship with pushforwards. | |
| Oct 12, 2011 at 0:50 | comment | added | Anatoly Preygel | Re 1, elaborating on Daniel's comment: If you rationalize on both sides, this is asking to compare rational Chow theory with rational even-dimensional cohomology. In general, that won't go well (e.g., for $X$ a positive genus curve). It will be true only under some very restrictive hypotheses on $X$ (e.g., if $X$ is "cellular" in the sense of a locally closed decomposition by affine spaces). The result of Thomason is saying that things in fact get better if you look at higher and higher K-theory and look at torsion(/complete) instead of rationalizing. | |
| Oct 12, 2011 at 0:39 | answer | added | Alexander Braverman | timeline score: 4 | |
| Oct 12, 2011 at 0:02 | comment | added | Kevin H. Lin | Well, I'm not looking at graded anything. That is, I'm only looking at $K^0$. | |
| Oct 11, 2011 at 23:24 | comment | added | Daniel Pomerleano | I know next to nothing but I think that the answer is that this is very rarely an isomorphism... it doesn't seem like the left side is two periodic in any way. If you invert the Bott element than you get closer. Here is are some papers that describes a lot of intricate relationships related to this question: archive.numdam.org/ARCHIVE/ASENS/ASENS_1985_4_18_3/… math.unl.edu/~mwalker5/papers/finite.pdf | |
| Oct 11, 2011 at 21:59 | history | asked | Kevin H. Lin | CC BY-SA 3.0 |