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Torsion birational motives of surfaces and unramified cohomology | | Kanetomo Sato
; Takao Yamazaki
; | | Date: |
1 Sep 2023 | | Abstract: | 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 $T o S$ 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 $S imes S$ violates the integral
Hodge conjecture. | | Source: | arXiv, 2309.00430 | | Services: | Forum | Review | PDF | Favorites | |
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