Torsion birational motives of surfaces and unramified cohomology
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914252552404992 |
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| author | Sato, Kanetomo Yamazaki, Takao |
| author_facet | Sato, Kanetomo Yamazaki, Takao |
| contents | Let $S$ and $T$ be smooth projective varieties over an algebraically closed field. Suppose that $S$ is a surface admitting a decomposition of the diagonal. We show that, away from the characteristic of $k$, if an algebraic correspondence $T \to S$ acts trivially on the unramified cohomology, then it acts trivially on any normalized, birational, and motivic functor. This generalizes Kahn's result on the torsion order of $S$. We also exhibit an example of $S$ over $\mathbb{C}$ for which $S \times S$ violates the integral Hodge conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00430 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Torsion birational motives of surfaces and unramified cohomology Sato, Kanetomo Yamazaki, Takao Algebraic Geometry K-Theory and Homology Number Theory 14C15 (Primary) 14M20, 19E15 (Secondary) Let $S$ and $T$ be smooth projective varieties over an algebraically closed field. Suppose that $S$ is a surface admitting a decomposition of the diagonal. We show that, away from the characteristic of $k$, if an algebraic correspondence $T \to S$ acts trivially on the unramified cohomology, then it acts trivially on any normalized, birational, and motivic functor. This generalizes Kahn's result on the torsion order of $S$. We also exhibit an example of $S$ over $\mathbb{C}$ for which $S \times S$ violates the integral Hodge conjecture. |
| title | Torsion birational motives of surfaces and unramified cohomology |
| topic | Algebraic Geometry K-Theory and Homology Number Theory 14C15 (Primary) 14M20, 19E15 (Secondary) |
| url | https://arxiv.org/abs/2309.00430 |