Bounding Cubic-triple Product Selmer Groups of Elliptic Curves
نویسنده
چکیده
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.
منابع مشابه
Hirzebruch–Zagier cycles and twisted triple product Selmer groups
Let E be an elliptic curve over Q and A another elliptic curve over a real quadratic number field. We construct a Q-motive of rank 8, together with a distinguished class in the associated Bloch–Kato Selmer group, using Hirzebruch–Zagier cycles, that is, graphs of Hirzebruch–Zagier morphisms. We show that, under certain assumptions on E and A, the non-vanishing of the central critical value of t...
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تاریخ انتشار 2015