Thiago Landim (IMJ): Weights and motives on stacks

The existence of a motivic t-structure is an old problem in the center of many conjectures related with algebraic cycles. Inspired by Deligne, Bondarko defined a dual notion, now called weight structure, and proved Beilinson motives (and later integral cdh-motives) on nice schemes admit weight structures. In this talks, we are going to prove the category of K-motives (modules of genuine K-theory inside motivic spectra) on tame quotient stacks, as defined by Hoyois, admits a well-behaved category of geometric motives and prove the existence of bounded weight structure on them. If time allows, we are going to explain how this behaves better for Kan extended theories, e.g. cdh-motives, and how étale sheaves behaves even better.

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