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Jul 9, 2017 at 13:01 vote accept Wenzhe
Jul 1, 2017 at 6:05 comment added Mikhail Bondarko I would recommend you to contact either Leonid Positselski (positselski.narod.ru, positselski at yandex dot ru) or Sasha Beilinson.
Jun 30, 2017 at 19:22 comment added Mikhail Bondarko It's easy to believe that certain conjectures on the "motivic Hopf algebra" imply the statement you are interested in. Yet I doubt that anybody has written this down carefully.
Jun 30, 2017 at 15:15 comment added Wenzhe Thank you very much. Ayoub's in his paper a guide to (etale) motivic sheaves gives an ambiguous remark 5.8, i.e. conjecture A and conjecture B, in his paper "L'algebre de Hopf et le groupe de Galois motiviques d'un corps de caracteristique nulle, I." should imply the t structure conjecture of $\textbf{DA}^{et}_{ct}(S,\Lambda)$ andmore, "by more, we have in mind the property that $\textbf{DA}^{et}_{ct}(S,\Lambda)$ is equivalent to the derived category of the heart of its motivic t-structure ". Do you know whether this "more" has been proved or not?
Jun 30, 2017 at 14:34 history answered Mikhail Bondarko CC BY-SA 3.0