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On log motives
Tetsushi Ito, Kazuya Kato, Chikara Nakayama and Sampei Usui |
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Vol. 2 (2020), No. 4, 733–789
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Abstract |
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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. |
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Keywords
motive, mixed motive, log geometry
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Mathematical Subject Classification 2010
Primary: 14C15
Secondary: 14A20, 14F20
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Milestones
Received: 25 December 2017
Revised: 12 April 2019
Accepted: 24 June 2019
Published: 10 December 2019
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Authors |
| Tetsushi Ito | |
| Department of Mathematics Kyoto University Kyoto Japan |
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| Kazuya Kato | |
| Department of Mathematics University of Chicago Chicago, IL United States |
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| Chikara Nakayama | |
| Department of Economics Hitotsubashi University Kunitachi Tokyo Japan |
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| Sampei Usui | |
| Graduate School of Science Osaka University Toyonaka, Osaka Japan |
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