Timeline for How is K-theory defined for coherent sheaves?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Aug 1, 2010 at 17:02 | vote | accept | babubba | ||
| Jul 26, 2010 at 21:02 | answer | added | mark | timeline score: 6 | |
| Jul 7, 2010 at 17:50 | comment | added | Graham Leuschke | To see that they're not the same, consider the toy example $R=k[t]/(t2)$. There are only two indecomposable f.g. modules, namely $R$ itself and the residue field $k$. If you're killing relations from exact sequences, you have $[R]=2[k]$ so $L$ is $\mathbb{Z}$. If you're only killing direct−sum relations then you get $\mathbb{Z}^2$. | |
| Jul 7, 2010 at 14:35 | comment | added | t3suji | This is pretty standard, but amazingly the standard online refs do not seem to have clear answers in obvious places. Answers are "No" and "L(A)" respectively. For fun, one can try computing the groups when $X$ is the projective line. | |
| Jul 7, 2010 at 12:36 | history | edited | babubba |
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| Jul 7, 2010 at 12:14 | history | asked | babubba | CC BY-SA 2.5 |