Bounding cubic-triple product Selmer groups of elliptic curves

Yifeng Liu

Bounding cubic-triple product Selmer groups of elliptic curves

Number Theory 2017-02-02 v2

Authors: Yifeng Liu

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 $0$ .

Keywords

elliptic curves Selmer groups cubic-triple product Bloch-Kato Selmer groups L-functions modular elliptic curves

Cite

@article{arxiv.1511.08268,
  title  = {Bounding cubic-triple product Selmer groups of elliptic curves},
  author = {Yifeng Liu},
  journal= {arXiv preprint arXiv:1511.08268},
  year   = {2017}
}

Comments

78 pages, major revision

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