Timeline for H_3 of SL(n,Z) and SL(n,F_p)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2017 at 6:49 | comment | added | მამუკა ჯიბლაძე | @Theo Right, I had this in mind. It requires quite a lot of previous material though - calculation of $K_2(\mathbb Z)$ (IV.5.2.2), $K_3(\mathbb Z)$ (VI.10) and the multiplication $\{-1,\_,\_\}$ (1.19) and (1.20) as well as $K$-theory of finite fields (1.13) | |
| Jan 2, 2017 at 2:23 | vote | accept | Sarah | ||
| Jan 1, 2017 at 22:44 | comment | added | Theo Johnson-Freyd | @მამუკაჯიბლაძე I couldn't find this at the location you suggested, although I don't have the published version available. There is an Exercise 1.20 in Chapter IV on page 16 of math.rutgers.edu/~weibel/Kbook.html, which I think would be page 299 of the book. Probably you mean that these answers can be extracted from Chaper IV Corollary 1.20? Do you mind providing more instruction? I have left a CW answer you could edit, or you could leave a complete answer on your own. | |
| Jan 1, 2017 at 22:40 | answer | added | Theo Johnson-Freyd | timeline score: 17 | |
| Jan 1, 2017 at 5:27 | comment | added | მამუკა ჯიბლაძე | Quickest reference is probably 4.1.20 in Weibel's K-book (page 299 there): for integers it gives what @Theo says, for a finite field with $q$ elements --- $\mathbb Z/(q^2-1)\mathbb Z$ (stabilization is from $n=3$ on) | |
| Jan 1, 2017 at 4:59 | comment | added | Theo Johnson-Freyd | I happen to remember that H_3(SL_2(3)) = Z/24, in case that helps. This number 24 shows up a lot. | |
| Jan 1, 2017 at 4:58 | comment | added | Theo Johnson-Freyd | I don't know the F_p case. If memory serves, H_3(SL_n(Z)) = Z/24 for n large. I left this as a comment rather than answer both because I am missing the F_p case and because I don't have a reference handy. (I can dig for one if needed.) | |
| Jan 1, 2017 at 4:05 | history | edited | GH from MO |
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| Jan 1, 2017 at 2:52 | review | First posts | |||
| Jan 1, 2017 at 7:08 | |||||
| Jan 1, 2017 at 2:48 | history | asked | Sarah | CC BY-SA 3.0 |