Timeline for Higher descent cohomology
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2013 at 21:17 | comment | added | Jonathan Beardsley | No worries, thanks for your answer! I think very few people are familiar with the notion of descent cohomology that I want to discuss. It's unfortunate, because I think it's an interesting notion. The story most certainly does not end with classifying morphisms which are effective descent morphisms. | |
| Dec 20, 2013 at 18:49 | comment | added | David White | I don't know anything about Mesablishvili's work, and I guess I missed that this was the thing you wanted an $\infty$-categorical analogue of. Sorry my answer was something you already knew. I have no idea where in Lurie's work to search for this. Whenever I'm in that position I just ask Dylan or Akhil. | |
| Dec 20, 2013 at 18:46 | comment | added | Jonathan Beardsley | Where by group and co-group cohomology I really mean homotopy fixed points spectral sequence or homotopy co-fixed points spectral sequence (which is NOT homotopy orbits!!). | |
| Dec 20, 2013 at 18:44 | comment | added | Jonathan Beardsley | I should add that Galois cohomology and Hopf-Galois cohomology descent spectral sequences (e.g. the Adams Novikov Spectral Sequence) both follow as a special case of the situation I'm describing. It's just that in those cases, the relevant equivalences allow one to identify the Amitsur cohomology as a group or co-group cohomology. | |
| Dec 20, 2013 at 18:42 | comment | added | Jonathan Beardsley | Thanks David. I'm pretty familiar with that paper. Unfortunately, she does not construct a descent cohomology sort of thing in her work, though one could certainly see a way to do it in her framework. I'm hoping to find some way to do this in terms of $\infty$-categories just because I don't really know how to put model category structures on things that don't support obvious left Quillen functors from something I already know about. However, I think the idea is the same from both points of view. | |
| Dec 20, 2013 at 15:34 | history | answered | David White | CC BY-SA 3.0 |