Universal Weil cohomology
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915131853635584 |
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| author | Barbieri-Viale, L. Kahn, B. |
| author_facet | Barbieri-Viale, L. Kahn, B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Weil cohomology Barbieri-Viale, L. Kahn, B. Algebraic Geometry Category Theory K-Theory and Homology Number Theory 18F99, 14F99 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. |
| title | Universal Weil cohomology |
| topic | Algebraic Geometry Category Theory K-Theory and Homology Number Theory 18F99, 14F99 |
| url | https://arxiv.org/abs/2401.14127 |