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arXiv · 2501.14106

Mixed Motives

L. Barbieri-Viale
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Abstract

A mixed Weil cohomology with values in an abelian rigid tensor category is a cohomological functor on Voevodsky's category of motives which is satisfying K\"unneth formula and such that its restriction to Chow motives is a Weil cohomology. We show that the universal mixed Weil cohomology exists. Nori motives can be recovered as a universal enrichment of Betti cohomology via a localisation. This new picture is drawing some consequences with respect to the theory of mixed motives in arbitrary characteristic.

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L. Barbieri-Viale. 2025-01-23. Mixed Motives. https://doi.org/10.1016/j.indag.2025.03.002

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