Timeline for Constructions of motivic complex that is only supported on positive degrees
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| Sep 22, 2022 at 8:00 | comment | added | user127776 | @D.-C.Cisinski Thanks. Indeed the construction is designed in a way so the cohomologies satisfy Gersten type resolution. This is super interesting it seems to me that homotopy invariance is the only obstruction to prove this conjecture. The rest of follows from a Geisser-Levine type argument using polyrelative versions of the cohomology. Even the construction of a map from this cohomology to the motivic one follows from it. One also needs to carefully check the groups in Goncharov's complex applied to $\hat{\Delta}^{\bullet}$ (simplices semi-localized at the vertices) is exact (it seems to be) | |
| Sep 21, 2022 at 8:36 | comment | added | D.-C. Cisinski | The key word here might be: coniveau spectral sequence, e.g. see here: webusers.imj-prg.fr/~bruno.kahn/preprints/bo.pdf The first page is a Cousin complex, and the Beilinson-Soulé vanishing conjecture will make this spectral sequence degenerate to the point where it provides a resolution of motivic cohomology. In other words, you can mimick what is done in this paper numdam.org/item/AFST_2014_6_23_3_591_0 replacing Weil cohomologies by motivic cohomology (and working in the heart of the putative motivic t-structure). | |
| Sep 21, 2022 at 4:01 | history | edited | user127776 | CC BY-SA 4.0 |
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| Sep 21, 2022 at 3:46 | history | edited | user127776 | CC BY-SA 4.0 |
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| Aug 1, 2022 at 20:59 | history | asked | user127776 | CC BY-SA 4.0 |