Unramified logarithmic Hodge–Witt cohomology and -invariance

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...

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Bibliographic Details
Published inForum of mathematics. Sigma Vol. 10
Main Authors Kai, Wataru, Otabe, Shusuke, Yamazaki, Takao
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.01.2022
Subjects
Homology
Invariants
Isomorphism
Reciprocity
Sheaves
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Summary: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.
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ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2022.6