Timeline for Spectral sequence from resolution of condensed abelian groups
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2020 at 9:31 | comment | added | Dustin Clausen | Yes, Yemon. I don't know what it's called, but that's what it is. | |
| Dec 17, 2020 at 21:48 | comment | added | Yemon Choi | @DustinClausen Is this what "homological cavemen" like myself might call hyper(co)homology? i.e. take a projective resolution of each $P_i$ and then take the (co)homology of the total complex? | |
| Dec 17, 2020 at 21:07 | comment | added | Dustin Clausen | You can also think of it like this. If it were a projective resolution, we could use it to calculate $Ext^i(\mathbb{R},A)$ in terms of $Hom(P_i,A)$. The spectral sequence is saying that even when the terms are not projective, you can still in some sense calculate $Ext^i(\mathbb{R},A)$ in terms of not just $Hom(P_i,A)$, but $RHom(P_i,A)$. I think this plus the special case where there are only 2 terms mentioned above give the "feel" for this sort of thing. | |
| Dec 17, 2020 at 21:06 | history | edited | Sofía Marlasca Aparicio | CC BY-SA 4.0 |
added 27 characters in body
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| Dec 17, 2020 at 21:02 | comment | added | Dustin Clausen | Exactly, he means the spectral sequence for $Ext^i(-,A)$ coming from the "stupid" filtration on the resolution (without the $\mathbb{R}$ term) induced by truncation. If there were only two terms in the resolution, this would be the same as the induced long exact sequence on $Ext^i(-,A)$. | |
| Dec 17, 2020 at 20:49 | review | First posts | |||
| Dec 18, 2020 at 4:46 | |||||
| Dec 17, 2020 at 20:42 | history | asked | Sofía Marlasca Aparicio | CC BY-SA 4.0 |