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Let be a modular elliptic curve over a totally real cubic field. We have a cubic-triple product motive over constructed from through multiplicative induction; it is of rank 8. We show that, under certain assumptions on , the nonvanishing of the central critical value of the -function attached to the motive implies that the dimension of the associated Bloch-Kato Selmer group is 0.
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Yifeng Liu, Bounding cubic-triple product Selmer groups of elliptic curves. J. Eur. Math. Soc. 21 (2019), no. 5, pp. 1411–1508DOI 10.4171/JEMS/865