Timeline for $K_2$ over finite fields and polynomials over finite fields
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| yesterday | comment | added | Andy Putman | @NoahG.Singer: That's correct. You're looking at what is called "unstable" $K_2$, and in his book Milnor computes $K_2(\mathbb{Z})$ by first making an unstable computation. | |
| yesterday | history | edited | Noah G. Singer | CC BY-SA 4.0 |
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| 2 days ago | vote | accept | Noah G. Singer | ||
| 2 days ago | comment | added | Noah G. Singer | One note: The notation $K_2$ seems to refer to the direct limit of the quotients as $n \to \infty$. I am interested in the case of fixed $n$ (say, $n=3$) so it is not technically sufficient to just show $K_2$ is trivial. However, looks like e.g. Milnor's techniques probably work for the $n=3$ case directly? | |
| Dec 9 at 1:35 | comment | added | Andy Putman | If this kind of thing is going to come up in your work repeatedly, it's worth knowing some rudiments of algebraic K-theory. Milnor's short book on the subject starts at the beginning and is basically self-contained (modulo standard graduate algebra stuff). I've had many graduate students read it. Lots of more recent books focus on stuff with a more algebraic topology flavor, so they're probably harder for outsiders to read. | |
| Dec 8 at 3:31 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
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| Dec 8 at 3:21 | answer | added | F Zaldivar | timeline score: 4 | |
| Dec 7 at 20:56 | answer | added | user509184 | timeline score: 8 | |
| Dec 7 at 19:41 | comment | added | Matthias Wendt | Milnor in his paper "Algebraic K-theory and quadratic forms" explains the vanishing of $K_2$ of finite fields in Example 1.5. It's an algebraic consequence of $K_1$ being cyclic. For the polynomial ring case, some more theory is needed. | |
| Dec 7 at 18:35 | history | edited | Noah G. Singer | CC BY-SA 4.0 |
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| Dec 7 at 18:31 | comment | added | Noah G. Singer | E.g., I found this survey: cs.ox.ac.uk/people/david.mestel/essay.pdf for $\mathbb{F}_q$. I am hoping for a simpler proof in the case where we only care about $K_2$. | |
| Dec 7 at 18:28 | history | asked | Noah G. Singer | CC BY-SA 4.0 |