Unramified logarithmic Hodge–Witt cohomology and $\mathbb {P}^1$-invariance
Forum of Mathematics, Sigma, Tome 10 (2022)
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Let X be a smooth proper variety over a field k and suppose that the degree map ${\mathrm {CH}}_0(X \otimes _k K) \to \mathbb {Z}$ is isomorphic for any field extension $K/k$. We show that $G(\operatorname {Spec} k) \to G(X)$ is an isomorphism for any $\mathbb {P}^1$-invariant Nisnevich sheaf with transfers G. This generalises a result of Binda, Rülling and Saito that proves the same conclusion for reciprocity sheaves. We also give a direct proof of the fact that the unramified logarithmic Hodge–Witt cohomology is a $\mathbb {P}^1$-invariant Nisnevich sheaf with transfers.
@article{10_1017_fms_2022_6,
author = {Wataru Kai and Shusuke Otabe and Takao Yamazaki},
title = {Unramified logarithmic {Hodge{\textendash}Witt} cohomology and $\mathbb {P}^1$-invariance},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.6},
language = {en},
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AU - Wataru Kai
AU - Shusuke Otabe
AU - Takao Yamazaki
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Wataru Kai; Shusuke Otabe; Takao Yamazaki. Unramified logarithmic Hodge–Witt cohomology and $\mathbb {P}^1$-invariance. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.6
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