Timeline for Relation between local cohomology and open immersions
Current License: CC BY-SA 3.0
9 events
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| Dec 29, 2016 at 19:33 | comment | added | nfdc23 | No, but for reasonably interesting classes of maps (such as proper ones) between reasonable noetherian schemes (say finite type over a regular ring) one has robust coherent duality and so on. The point is just that for various interesting classes of geometric objects there are hard theorems in the direction of "six-functors" formalism, and you should learn how some of those proofs work to appreciate what the real difficulties are in setting up the hard parts of such formalism and in particular why asking for things in the total generality of locally ringed spaces is asking for too much. | |
| Dec 29, 2016 at 1:25 | comment | added | Saal Hardali | @nfdc23 Are you claiming that noetherian schemes have six functors? | |
| Dec 29, 2016 at 1:21 | comment | added | nfdc23 | I think it is a bit naive. Hard work is needed to make such things in various interesting cases, such as with noetherian schemes, complex-analytic spaces, suitable non-archimedean analytic spaces, etc. It is hard to imagine that some abstract nonsense would unify all of these. Is there an actual motivating reason or just idle curiosity behind that question? I recommend to learn the substance behind one of the frameworks where the 6-functor formalism exists, and then you will better appreciate the key issues involved. A general locally ringed space is too featureless for what needs to be done. | |
| Dec 29, 2016 at 1:17 | comment | added | Saal Hardali | @nfdc23 Sounds nice, I'll try. You might have something to say about the following question: mathoverflow.net/questions/257539/… | |
| Dec 29, 2016 at 1:14 | comment | added | nfdc23 | Read Expose I of SGA2 for a version with arbitrary topological spaces (not specifically tied up with quasi-coherent sheaves on schemes). | |
| Dec 29, 2016 at 0:49 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Dec 28, 2016 at 23:29 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Dec 28, 2016 at 23:18 | vote | accept | Saal Hardali | ||
| Dec 28, 2016 at 23:17 | history | answered | Saal Hardali | CC BY-SA 3.0 |