Vol. 2, No. 4, 2020

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On log motives

Tetsushi Ito, Kazuya Kato, Chikara Nakayama and Sampei Usui

Vol. 2 (2020), No. 4, 733–789
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 the latter being a Tannakian category. We discuss various realizations, formulate Tate and Hodge conjectures, and verify them in the curve case.

Keywords
motive, mixed motive, log geometry
Mathematical Subject Classification 2010
Primary: 14C15
Secondary: 14A20, 14F20
Milestones
Received: 25 December 2017
Revised: 12 April 2019
Accepted: 24 June 2019
Published: 10 December 2019
Authors
Tetsushi Ito
Department of Mathematics
Kyoto University
Kyoto
Japan
Kazuya Kato
Department of Mathematics
University of Chicago
Chicago, IL
United States
Chikara Nakayama
Department of Economics
Hitotsubashi University
Kunitachi
Tokyo
Japan
Sampei Usui
Graduate School of Science
Osaka University
Toyonaka, Osaka
Japan