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 Künneth 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.
Mixed motives / L. Barbieri-Viale. - In: INDAGATIONES MATHEMATICAE. - ISSN 0019-3577. - 37:1(2026 Jan), pp. 399-420. [10.1016/j.indag.2025.03.002]
Mixed motives
L. Barbieri-Viale
2026
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 Künneth 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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