Open Access
March 2014 Heights of motives
Kazuya Kato
Proc. Japan Acad. Ser. A Math. Sci. 90(3): 49-53 (March 2014). DOI: 10.3792/pjaa.90.49


We define the height of a motive over a number field. We show that if we assume the finiteness of motives of bounded height, Tate conjecture for the $p$-adic Tate module can be proved for motives with good reduction at $p$.


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Kazuya Kato. "Heights of motives." Proc. Japan Acad. Ser. A Math. Sci. 90 (3) 49 - 53, March 2014.


Published: March 2014
First available in Project Euclid: 27 February 2014

zbMATH: 1314.14048
MathSciNet: MR3178484
Digital Object Identifier: 10.3792/pjaa.90.49

Primary: 14G40
Secondary: 11G50 , 14G25

Keywords: $p$-adic Hodge theory , Height , Hodge theory , motive , Tate conjecture

Rights: Copyright © 2014 The Japan Academy

Vol.90 • No. 3 • March 2014
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