On log motives
Algebraic Geometry
2019-12-18 v1
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.
Cite
@article{arxiv.1712.09815,
title = {On log motives},
author = {Tetsushi Ito and Kazuya Kato and Chikara Nakayama and Sampei Usui},
journal= {arXiv preprint arXiv:1712.09815},
year = {2019}
}