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

Abstract

We define ket abelian schemes, ket 1-motives, and ket log 1-motives, and formulate duality theory for these objects. Then we show that tamely ramified strict 1-motives over a complete discrete valuation field can be extended to ket log 1-motives over the corresponding discrete valuation ring. As an application, we present a proof to a result of Kato stated in one of his preprint without proof.