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Extending tamely ramified strict 1-motives into két log 1-motives
Published online by Cambridge University Press: 09 March 2021
Abstract
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
- Type
- Algebraic and Complex Geometry
- Information
- Creative Commons
- 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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