Timeline for Voevodsky's six functor formalism VS Lucas Mann's
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| May 23 at 14:46 | history | edited | Emily |
edited tags
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| Feb 14, 2023 at 8:03 | vote | accept | Ola Sande | ||
| Feb 13, 2023 at 22:11 | answer | added | Marc Hoyois | timeline score: 29 | |
| Feb 13, 2023 at 21:55 | comment | added | Marc Hoyois | @AlexeyDo The book by Cisinski and Déglise is not independent from Ayoub's thesis: it uses the main result of the latter as a black box. | |
| Feb 13, 2023 at 19:40 | history | edited | Jérôme Poineau | CC BY-SA 4.0 |
corrected spelling in the title
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| S Feb 13, 2023 at 14:10 | history | suggested | Z. M | CC BY-SA 4.0 |
Seemingly, the OP is refereing to the first part of Ayoub's thesis. Edited the link.
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| Feb 13, 2023 at 14:08 | comment | added | Alexey Do | If you find Ayoub's thesis is incredibly difficult (in fact it is), you may want to take a look at Cisinski book "Triangulated categories of mixed motives" and Ayoub's ICM talk 2014. | |
| Feb 13, 2023 at 14:05 | comment | added | Alexey Do | @TimothyChow, I have not checked Mann's thesis in details, but Ayoub also defined (in the rigid context) the rigid stable homotopy category of a scheme and the corresponding six functors. I guess that Mann's results would not surprise Voevodsky. Almost every six functors behave similar to the étale case. There are few "slight" differences in Ayoub's thesis compared to étale world. For instance, his constructions rely heavily on Thom equivalence or one has to prove the projective base change theorem and then the proper one and then defining the proper push forward operation. | |
| Feb 13, 2023 at 13:56 | comment | added | Alexey Do | @DavidLoeffler, according to a post òd Weibel on AMS, Voevodsky gave a lecture on six functors formalism in 2001-2002, but never published his results. Later Ayoub figured it out and published it in his thesis. | |
| Feb 13, 2023 at 9:00 | comment | added | Z. M | My first understanding is that, modulo technical differences between $\infty$-categories and 2-categorical truncations, Ayoub's formalism only needs the data $f^*$, and imposes some form of $\mathbb A^1$-invariance, recovering $f_!$ from some form of Thom isomorphism, but in Mann's formalism, $f_!$'s are separate data. It is also unclear to me how Ayoub's thesis deals with the monoidal structure. | |
| Feb 13, 2023 at 8:33 | review | Suggested edits | |||
| S Feb 13, 2023 at 14:10 | |||||
| Feb 13, 2023 at 6:08 | comment | added | David Loeffler | Did Voevodsky in fact have a 6-functor formalism? I was under the impression that this was one of the main new results Ayoub himself proved in his thesis. | |
| Feb 12, 2023 at 23:42 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added links
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| Feb 12, 2023 at 21:43 | history | edited | Ola Sande | CC BY-SA 4.0 |
added 1 character in body
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| Feb 12, 2023 at 21:42 | history | undeleted | Ola Sande | ||
| Feb 12, 2023 at 21:39 | history | deleted | Ola Sande | via Vote | |
| Feb 12, 2023 at 21:34 | history | asked | Ola Sande | CC BY-SA 4.0 |