On log motives

Tetsushi Ito, Kazuya Kato, Chikara Nakayama, Sampei Usui
2020 Tunisian Journal of Mathematics  
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 the latter being a Tannakian category. We discuss various realizations, formulate Tate and Hodge conjectures, and verify them in the curve case. MSC2010: primary 14C15; secondary 14A20, 14F20.
doi:10.2140/tunis.2020.2.733 fatcat:ze3cmsvgzjfwzjnwciyvibwj4a