Bounding cubic-triple product Selmer groups of elliptic curves

Abstract

Let E be a modular elliptic curve over a totally real cubic field. We have a cubic-triple product motive over 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.