Year: 2014
Type: article
Abstract: 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∞-Selmer group of E over any strongly admissible p-adic Lie extension K∞/K under the assumption that it is a torsion module over the Iwasawa algebra of the Galois group G = Gal(K∞/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.
Authors: Tibor Backhausz, Gergely Zábrádi
Institutions: University of Cambridge, Eötvös Loránd University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2012589819