2024/01/25 by Luca Barbieri-Viale, Barbieri-Viale, L., Bruno Kahn +1
Mathematics · #14F99 #18F99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2401.14127
openalex publication_date 2024/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 André's category of motives for motivated correspondences and show that it has a universal property. This theory extends over suitable bases.