Bounding cubic-triple product Selmer groups of elliptic curves

Yifeng Liu

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arXiv · 1511.08268

Bounding cubic-triple product Selmer groups of elliptic curves

Yifeng Liu

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Abstract

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 non-vanishing 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 $0$.

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Yifeng Liu. 2017-01-31. Bounding cubic-triple product Selmer groups of elliptic curves. https://arxiv.org/abs/1511.08268

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