Journal of the European Mathematical Society


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Volume 21, Issue 5, 2019, pp. 1411–1508
DOI: 10.4171/JEMS/865

Published online: 2019-02-01

Bounding cubic-triple product Selmer groups of elliptic curves

Yifeng Liu[1]

(1) Yale University, New Haven, USA

Let $E$ be a modular elliptic curve over a totally real cubic field. We have a cubic-triple product motive over $\mathbb{Q}$ constructed from $E$ through multiplicative induction; it is of rank 8. We show that, under certain assumptions on $E$, the nonvanishing of the central critical value of the $L$-function attached to the motive implies that the dimension of the associated Bloch-Kato Selmer group is 0.

Keywords: Selmer group, Bloch–Kato conjecture, elliptic curve

Liu Yifeng: Bounding cubic-triple product Selmer groups of elliptic curves. J. Eur. Math. Soc. 21 (2019), 1411-1508. doi: 10.4171/JEMS/865