Characteristic elements, pairings and functional equations over the false Tate curve extension
Characteristic elements, pairings and functional equations over the false Tate curve extension
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假泰特曲线延伸的特征元素、配对和函数方程
DOI：
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发表时间：
2008
影响因子：
0.8
通讯作者：
Gergely Zábrádi
中科院分区：
文献类型：
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作者：
Gergely Zábrádi
摘要我们在p≥5的椭圆曲线的伪Tate曲线延拓上构造了对偶塞尔默群上的一个对偶对，该对偶对具有良好的普通约化。这就给出了一个与p-adic L-函数的特征元函数方程相容的特征元函数方程。作为一个应用程序，我们计算这些模块的特征元素-自然产生的岩泽理论椭圆曲线的假泰特曲线的扩展-其中有秩1的子组的伽罗瓦组固定的分圆扩展的地面字段。我们还表明，一个非主自反左理想的Iwasawa代数的例子不排除的可能性，所有的扭转Iwasawa-模是伪同构的代数的直和的主理想。
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.