Timeline for K(F_1) = sphere spectrum?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2009 at 13:42 | comment | added | Peter Arndt | @Reid:What one usually does to count F1-points, when the number of points of a variety is given by a polynomial (which is not unusual), is to "multiply away" the zeros at q=1 and then insert 1. This then is consistent with the symmetry group of the chamber view point - for any Chevalley group not only GLn. | |
| Oct 24, 2009 at 13:41 | comment | added | Peter Arndt | @harrison: Yes, burnside ring and representation ring, marks and characters, etc. behave very similarly. Even some proofs carry over, e.g. Steinberg adapted a proof of Frobenius about the irreducibility of some permutation representation to the linear representation analogon (I saw this in a lecture by C. Soule, Nashville 2009) | |
| Oct 21, 2009 at 18:10 | comment | added | Reid Barton | Is GLn(F1) = Sigma_n right? The cardinality doesn't work out when I take the q->1 limit of |GLn(Fq)| (off by a factor of (q-1)^n). | |
| Oct 21, 2009 at 17:58 | comment | added | Harrison Brown | I don't have a direct reference to this, but if you compare representation theory and the theory of group actions on finite sets, it seems to me that you can see more evidence that the correct way of thinking about F_1 involves forgetting about addition. | |
| Oct 21, 2009 at 12:43 | history | answered | Peter Arndt | CC BY-SA 2.5 |