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

TL;DR

This paper introduces ket log 1-motives and demonstrates that tamely ramified strict 1-motives over a complete discrete valuation field can be extended to these new objects, providing a new proof for a result of Kato.

Contribution

It defines ket abelian schemes, ket 1-motives, and ket log 1-motives, and establishes their duality theory, extending tamely ramified strict 1-motives into ket log 1-motives.

Findings

Extension of tamely ramified strict 1-motives to ket log 1-motives

Duality theory for ket abelian schemes and ket 1-motives

Proof of Kato's result using the new framework

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.