Unramified logarithmic Hodge–Witt cohomology and -invariance - Kai, Wataru; Otabe, Shusuke; Yamazaki, Takao (Forum of mathematics. Sigma, 2022)
Let X be a smooth proper variety over a field k and suppose that the degree map ${CH}_0(X \otimes _k K) → \mathbb {Z}$ is isomorphic for any field extension $K/k$ . We show that $G(\operatorname {Spec} k) → G(X)$ 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.