JournalsjemsVol. 21, No. 5pp. 1411–1508

Bounding cubic-triple product Selmer groups of elliptic curves

  • Yifeng Liu

    Yale University, New Haven, USA
Bounding cubic-triple product Selmer groups of elliptic curves cover

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Abstract

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

Cite this article

Yifeng Liu, Bounding cubic-triple product Selmer groups of elliptic curves. J. Eur. Math. Soc. 21 (2019), no. 5, pp. 1411–1508

DOI 10.4171/JEMS/865