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.

Section 2 and Section have been made more systematic under the suggestion from the referee. Introduction has been rewritten. Errors and typos have been corrected. The article is now 38 pages long

References in corpus (2)

• Logarithmic structures of Fontaine-Illusie. II
• Logarithmic abelian varieties, Part VI: Local moduli and GAGF

Cited by in corpus (2)

• Log p-divisible groups associated to log 1-motives
• The monodromy pairing for logarithmic 1-motifs