Algebraic functional equations and completely faithful Selmer groups

作者：Backhausz Tibor^*; Zabradi Gergely

来源：International Journal of Number Theory, 2015, 11(4): 1233-1257.

DOI：10.1142/S1793042115500670

• Selmer group
• elliptic curve
• pairing
• completely faithful
• functional equation

Let E be an elliptic curve - defined over a number field K - without complex multiplication and with good ordinary reduction at all the primes above a rational prime p >= 5. We construct a pairing on the dual p(infinity)-Selmer group of E over any strongly admissible p-adic Lie extension K-infinity/K under the assumption that it is a torsion module over the Iwasawa algebra of the Galois group G - Gal(K-infinity/K). Under some mild additional hypotheses, this gives an algebraic functional equation of the conjectured p-adic L-function. As an application, we construct completely faithful Selmer groups in case the p-adic Lie extension is obtained by adjoining the p-power division points of another non-CM elliptic curve A.