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

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

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