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Universal Weil cohomology (2401.14127v3)
Published 25 Jan 2024 in math.AG, math.CT, math.KT, and math.NT
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.