Characteristic elements, pairings and functional equations over the false Tate curve extension

Abstract

AbstractWe construct a pairing on the dual Selmer group over false Tate curve extensions of an elliptic curve with good ordinary reduction at a primep≥5. This gives a functional equation of the characteristic element which is compatible with the conjectural functional equation of thep-adicL-function. As an application we compute the characteristic elements of those modules – arising naturally in the Iwasawa-theory for elliptic curves over the false Tate curve extension – which have rank 1 over the subgroup of the Galois group fixing the cyclotomic extension of the ground field. We also show that the example of a non-principal reflexive left ideal of the Iwasawa algebra does not rule out the possibility that all torsion Iwasawa-modules are pseudo-isomorphic to the direct sum of quotients of the algebra by principal ideals.