## 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.

Reference :

ArXiv link : https://arxiv.org/abs/2105.07433

Hal link :

##### Pdf :