Timeline for Some computational results and goals of stable motivic homotopy theory of schemes
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| Jul 31, 2020 at 21:32 | comment | added | D.-C. Cisinski | Such $\ell$-independence of traces is still a subject of research: this paper of Hiroki Kato arxiv.org/pdf/1904.02324.pdf for instance. However, the mere existence of motivic sheaves and fo their $\ell$-adic realizations make the independence of $\ell$ part of the aforementioned paper trivial. | |
| Jul 31, 2020 at 21:07 | comment | added | D.-C. Cisinski | I also wrote a survey which revists this kind of things here: mathematik.uni-regensburg.de/cisinski/traces.pdf (but many of this topic can be found in various remarks in my joint papers with Déglise). | |
| Jul 31, 2020 at 21:07 | comment | added | D.-C. Cisinski | I think independence of $\ell$ is a rather good topic to have in mind: a goal of the six operations in the motivic world is to promote many cohomological features of $\ell$-adic sheaves to the motivic world. Anything which is trace-like (Euler characteristics, zeta functions) falls in this category. A nice paper to read on these kind of features is Olsson's link.springer.com/article/10.1007/s00229-015-0765-3 (or math.berkeley.edu/~molsson/Chernandmotives4.0.pdf for free access). | |
| Jun 26, 2020 at 5:17 | comment | added | R. van Dobben de Bruyn | An obvious one that comes to mind is the Bloch–Kato conjecture (now a theorem of Voevodsky), which drove the development of $\mathbf A^1$-homotopy theory. Or are you asking specifically about the stable variant? | |
| Jun 26, 2020 at 2:54 | history | edited | user160214 | CC BY-SA 4.0 |
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| Jun 26, 2020 at 2:51 | review | First posts | |||
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| Jun 26, 2020 at 2:47 | history | asked | user160214 | CC BY-SA 4.0 |