Timeline for Generalized Teichmuller representatives
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S May 9, 2014 at 19:38 | history | edited | Nik Weaver | CC BY-SA 3.0 |
typo edited
|
| May 9, 2014 at 19:34 | review | Suggested edits | |||
| S May 9, 2014 at 19:38 | |||||
| Oct 24, 2009 at 1:47 | vote | accept | Qiaochu Yuan | ||
| Oct 24, 2009 at 1:47 | comment | added | Qiaochu Yuan | One can use the fact that for an integer matrix A we have tr(A^{p^k}) = tr(A^{p^{k-1})) mod p^k, which has a fairly straightforward proof using group actions. | |
| Oct 15, 2009 at 5:13 | comment | added | CJD | You're right about the trace description. I don't see anything better than that. Since Teichmüller reps aren't well-behaved with respect to addition, I wouldn't be surprised if that's the best you can do. If you changed addition to multiplication, then you'd probably get that the limit was the Teichmüller rep of the norm. Out of curiosity, how do you know that the limit exists? For my limits, I was using that if a = b mod p (resp. mod p^{1/e}), then a^{p^n} = b^{p^n} mod p^{1+n} (resp. mod ...). But I don't see how to use that for this sum. | |
| Oct 14, 2009 at 22:32 | comment | added | Qiaochu Yuan | Right, but it has a stronger property than that, namely being in Z_p and not just Z_q. What characterizes this element of Z_p? (I guess it's the trace of left multiplication by the Teichmuller representative of a on Z_q. Is that all one can say?) | |
| Oct 14, 2009 at 16:22 | history | answered | CJD | CC BY-SA 2.5 |