Unramified logarithmic Hodge-Witt cohomology and P1-invariance
Wataru Kai, Shusuke Otabe and Takao Yamazaki
Let $X$ be a smooth proper variety over a field $k$ and suppose that the degree map $\CH_0(X \otimes_k K) \to \Z$ is isomorphic for any field extension $K/k$. We show that $G(\Spec k) \to G(X)$ is an isomorphism for any $\P^1$-invariant Nisnevich sheaf with transfers $G$. This generalizes a result of Binda--R\"ulling--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 $\P^1$-invariant Nisnevich sheaf with transfers.
ArXiv link : https://arxiv.org/abs/2105.07433