Timeline for A lost lemma about periodicity in a grid of long exact sequences?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2022 at 10:37 | answer | added | John Rognes | timeline score: 1 | |
| Jan 16, 2017 at 20:06 | comment | added | ACL | It looks like it is the $3\times 3$ lemma (either for complexes in abelian categories, or in triangulated categories). | |
| Jan 4, 2013 at 17:05 | comment | added | Mariano Suárez-Álvarez | Re: your update: You can refer to this MO question! | |
| Jan 4, 2013 at 17:04 | history | edited | Johannes Nordström | CC BY-SA 3.0 |
Update clarifying the question
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| Jan 3, 2013 at 21:21 | answer | added | ubunke | timeline score: 2 | |
| Jan 3, 2013 at 21:12 | history | edited | Johannes Nordström | CC BY-SA 3.0 |
Corrected subscripts in statement of lemma
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| Jan 3, 2013 at 20:38 | answer | added | Eric Wofsey | timeline score: 4 | |
| Jan 3, 2013 at 20:32 | answer | added | Fernando Muro | timeline score: 4 | |
| Jan 3, 2013 at 20:25 | comment | added | Mariano Suárez-Álvarez | ... we really get a lot of isomorphisms. Maybe this is what you are seeing? (I am assuming everything converges; this should follow from the fact that your $C_{i,j}$ are bounded, I think!) | |
| Jan 3, 2013 at 20:24 | comment | added | Mariano Suárez-Álvarez | Look at your grid as a double complex, and let $C$ be the total complex. There is an action of $G=\mathbb Z$ on it by the translation you described, so we can compute hypercohomology $\mathbb H^\bullet(G,C)$. Using one of the two hypercohomology spectral sequences, we see is zero because of $C$ is exact; the other hypercohomology spectral sequence has then $E_2$ page looking like $H^\bullet(H^\bullet(\mathbb Z,C))$ and converges to zero. Since $\mathbb Z$ has global dimension $1$, this spectral sequence has only two rows (columns?) and degenerates at $E_3$; since the limit is zero, ... | |
| Jan 3, 2013 at 20:10 | comment | added | Mariano Suárez-Álvarez | $C_{23}$ should be $C_{13}$ and $C_{32}$ should be $C_{31}$ in the statement of the lemma, no? | |
| Jan 3, 2013 at 19:43 | history | asked | Johannes Nordström | CC BY-SA 3.0 |