  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.
