Mixed Motives
Algebraic Geometry
2025-08-27 v1 Category Theory
K-Theory and Homology
Number Theory
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.
Keywords
Cite
@article{arxiv.2501.14106,
title = {Mixed Motives},
author = {L. Barbieri-Viale},
journal= {arXiv preprint arXiv:2501.14106},
year = {2025}
}