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Extending tamely ramified strict 1-motives into két log 1-motives

Part of: Arithmetic algebraic geometry Abelian varieties and schemes Families, fibrations

Published online by Cambridge University Press:  09 March 2021

Heer Zhao Open the ORCID record for Heer Zhao [Opens in a new window]
Heer Zhao*
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen, Essen45117, Germany

Abstract

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We define két abelian schemes, két 1-motives and két log 1-motives and formulate duality theory for these objects. Then we show that tamely ramified strict 1-motives over a discrete valuation field can be extended uniquely to két log 1-motives over the corresponding discrete valuation ring. As an application, we present a proof to a result of Kato stated in [12, §4.3] without proof. To a tamely ramified strict 1-motive over a discrete valuation field, we associate a monodromy pairing and compare it with Raynaud’s geometric monodromy.

MSC classification

Primary: 14D06: Fibrations, degenerations
Secondary: 14K99: None of the above, but in this section 11G99: None of the above, but in this section
Type
Algebraic and Complex Geometry
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e20
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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