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 $p$.
"Heights of motives." Proc. Japan Acad. Ser. A Math. Sci. 90 (3) 49 - 53, March 2014. https://doi.org/10.3792/pjaa.90.49