Universal Weil cohomology

L. Barbieri-Viale; B. Kahn

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arXiv · 2401.14127

Universal Weil cohomology

L. Barbieri-Viale·B. Kahn

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Abstract

We construct a new Weil cohomology for smooth projective varieties over a field, universal among Weil cohomologies with values in rigid additive tensor categories. A similar universal problem for Weil cohomologies with values in rigid abelian tensor categories also has a solution. We give a variant for Weil cohomologies satisfying more axioms, like Weak and Hard Lefschetz. As a consequence, we get a different construction of Andr\'e's category of motives for motivated correspondences and show that it has a universal property. This theory extends over suitable bases.

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BibTeX RIS

L. Barbieri-Viale, B. Kahn. 2024-01-25. Universal Weil cohomology. https://arxiv.org/abs/2401.14127

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