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

Published online by Cambridge University Press:  01 May 2008

GERGELY ZÁBRÁDI
GERGELY ZÁBRÁDI*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB.
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Abstract

We construct a pairing on the dual Selmer group over false Tate curve extensions of an elliptic curve with good ordinary reduction at a prime p≥5. This gives a functional equation of the characteristic element which is compatible with the conjectural functional equation of the p-adic L-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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 3 , May 2008 , pp. 535 - 574
Copyright
Copyright © Cambridge Philosophical Society 2008

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