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

• Autores: Gergely Zábrádi
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 144, Nº 3, 2008, págs. 535-574
• Idioma: inglés
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• Resumen

  • 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.