Timeline for Who proved the motivic 6-functor formalism?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 19 at 8:26 | vote | accept | Ola Sande | ||
| Feb 10 at 21:52 | history | edited | LSpice | CC BY-SA 4.0 |
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| Feb 10 at 11:04 | history | edited | Marc Hoyois | CC BY-SA 4.0 |
added 22 characters in body
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| Feb 10 at 9:50 | comment | added | Peter Scholze | I agree with the update to the answer. Note also that in the rest of the talk, I was doing the same switch of notion related to what a 6FF is. (Somewhere I mumble something about the functor from Corr(Sch) not being part of the data in the construction of the (\infty,2)-category of motives.) | |
| Feb 10 at 6:37 | history | edited | Marc Hoyois | CC BY-SA 4.0 |
update based on comments
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| Feb 10 at 6:21 | comment | added | Marc Hoyois | @PeterScholze I see, then I will update my answer. Of course I have no issue with the universal property of Drew-Gallauer. What I am skeptical about is that SH is initial as a functor on correspondences satisfying some axioms that do not clearly force the !-functors to be what they are (which can be done with coh. properness/étaleness axioms or by using a suitable (∞,2)-category of correspondences). If you are referring to the "motivic sheaves" lecture, then I am indeed skeptical of the main theorem there for the same reason (even though it has a different set of axioms than in the question). | |
| Feb 9 at 20:41 | comment | added | Peter Scholze | Sorry, I did mean to cite Drew-Gallauer, but more in spirit than in details. When giving my course, I did convince myself that one can prove a precise initiality statement. The claim in the talk was meant to be slightly imprecise as during the discussion I was slightly shifting the intended meaning of 6-functor formalism; in particular, when working with the 2-category, I do not want to enforce a priori a functor from the correspondence category. (Relatedly, a uniqueness conjecture I made in my lecture notes is very likely false. Maybe this is why you are skeptical?) | |
| Feb 8 at 22:28 | comment | added | Marc Hoyois | I do not know how to prove it. In fact I am somewhat skeptical of the claim. I could imagine proofs of different claims about 2-categorical 6FFs or with additional axioms about cohomological properness/étaleness of proper morphisms/open immersions. | |
| Feb 8 at 22:21 | comment | added | Ola Sande | Do you know a vague idea of how the proof goes or how I can learn about it? (Just a guess: Does he somehow find that there exists some "universal "framed correspondence" (oo,n)- category" such that the (right-)lax symmetric monoidal functor form Cor(Sch_Z) to Pr^L that encodes the six functor formalism factors though it? (Sorry if the guess doesn't make sense. Then I'll think more about it:)) | |
| Feb 8 at 21:59 | comment | added | Marc Hoyois | Rather that the initial one is given by motivic spectra (the existence of an initial one should be formal). | |
| Feb 8 at 21:48 | comment | added | Ola Sande | And "the universal property of the 6FF of motivic spectra" is that there exists an initial one on Sch_Z? | |
| Feb 8 at 21:28 | history | answered | Marc Hoyois | CC BY-SA 4.0 |