Unramified logarithmic Hodge-Witt cohomology and -invariance

Wataru Kai; Shusuke Otabe; Takao Yamazaki

doi:10.1017/fms.2022.6

Unramified logarithmic Hodge-Witt cohomology and -invariance

Wataru Kai, Shusuke Otabe, Takao Yamazaki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let X be a smooth proper variety over a field k and suppose that the degree map is isomorphic for any field extension. We show that is an isomorphism for any -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 -invariant Nisnevich sheaf with transfers.

Original language	English
Article number	e19
Journal	Forum of Mathematics, Sigma
Volume	10
DOIs	https://doi.org/10.1017/fms.2022.6
Publication status	Published - 2022 Mar 16

Keywords

2020 Mathematics Subject Classification 14C15 14M20

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1017/fms.2022.6

Cite this

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abstract = "Let X be a smooth proper variety over a field k and suppose that the degree map is isomorphic for any field extension. We show that is an isomorphism for any -invariant Nisnevich sheaf with transfers G. This generalises a result of Binda, R{\"U}lling 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 -invariant Nisnevich sheaf with transfers.",

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author = "Wataru Kai and Shusuke Otabe and Takao Yamazaki",

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AU - Kai, Wataru

AU - Otabe, Shusuke

AU - Yamazaki, Takao

N1 - Funding Information: The first author is supported by a JSPS KAKENHI Grant (JP18K13382). The second author is supported by JSPS KAKENHI Grants (JP19J00366, JP21K20334). The third author is supported by JSPS KAKENHI Grants (JP18K03232, JP21K03153). Publisher Copyright: Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Nutrition Society.

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Y1 - 2022/3/16

N2 - Let X be a smooth proper variety over a field k and suppose that the degree map is isomorphic for any field extension. We show that is an isomorphism for any -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 -invariant Nisnevich sheaf with transfers.

AB - Let X be a smooth proper variety over a field k and suppose that the degree map is isomorphic for any field extension. We show that is an isomorphism for any -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 -invariant Nisnevich sheaf with transfers.

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Unramified logarithmic Hodge-Witt cohomology and -invariance

Abstract

Keywords

ASJC Scopus subject areas

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