Details

Autor(en) / Beteiligte

• Kai, Wataru
• Otabe, Shusuke
• Yamazaki, Takao

Titel

Unramified logarithmic Hodge–Witt cohomology and -invariance

Ist Teil von

• Forum of mathematics. Sigma, 2022, Vol.10, Article e19

Ort / Verlag

Cambridge: Cambridge University Press

Erscheinungsjahr

2022

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• Abstract 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.