Proceedings of the Japan Academy, Series A, Mathematical Sciences

Heights of motives

Kazuya Kato

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Abstract

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 $p$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 3 (2014), 49-53.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1393510214

Digital Object Identifier
doi:10.3792/pjaa.90.49

Mathematical Reviews number (MathSciNet)
MR3178484

Zentralblatt MATH identifier
1314.14048

Subjects
Primary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Secondary: 14G25: Global ground fields 11G50: Heights [See also 14G40, 37P30]

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

Citation

Kato, Kazuya. Heights of motives. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 3, 49--53. doi:10.3792/pjaa.90.49. https://projecteuclid.org/euclid.pja/1393510214


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References

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