Timeline for What are the higher homotopy groups of Spec Z ?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2013 at 5:56 | history | undeleted | Kim Morrison | ||
| Aug 21, 2012 at 7:22 | history | deleted | user631 | ||
| Nov 3, 2009 at 17:20 | comment | added | moonface | Oh, I see what you mean. Thanks for clarifying! | |
| Nov 3, 2009 at 15:02 | comment | added | Tyler Lawson | The word "represent" may not have been the best to use. No, it's not etale, but it's a sheaf on the etale site as the kernel of the map G_m -> G_m. (The cokernel, if I remember correctly, is isomorphic the direct image of the additive group on the etale site of Z/2.) | |
| Nov 3, 2009 at 13:52 | comment | added | moonface | \mu_2 is not etale over Spec(Z). | |
| Nov 3, 2009 at 12:23 | comment | added | Tyler Lawson | My memory is vague, but does H^3(X,G_m) = Q/Z imply that there are nontrivial elements in H^3(X,Z/2) arising from the kernel of the squaring map G_m -> G_m, since Z/2 and the 2nd roots of unity represent the same etale sheaf on this site? | |
| Nov 3, 2009 at 9:03 | comment | added | Ilya Nikokoshev |
Indeed H^i(X) is supposed to point out that X looks like a 3-sphere and it's not like homotopy groups of S^3 are easy.
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| Nov 3, 2009 at 6:38 | history | answered | user631 | CC BY-SA 2.5 |