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arXiv · 1712.09815

On log motives

Tetsushi Ito·Kazuya Kato·Chikara Nakayama·Sampei Usui
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Abstract

We define the categories of log motives and log mixed motives. The latter gives a new formulation for the category of mixed motives. We prove that the former is a semisimple abelian category if and only if the numerical equivalence and homological equivalence coincide, and that it is also equivalent to that the latter is a Tannakian category. We discuss various realizations, formulate Tate and Hodge conjectures, and verify them in curve case.

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Tetsushi Ito, Kazuya Kato, Chikara Nakayama, Sampei Usui. 2017-12-28. On log motives. https://doi.org/10.2140/tunis.2020.2.733

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