On the Refined Conjectures on Fitting Ideals of Selmer Groups of Elliptic Curves with Supersingular Reduction
On the Refined Conjectures on Fitting Ideals of Selmer Groups of Elliptic Curves with Supersingular Reduction
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椭圆曲线Selmer群超奇异约简拟合理想的细化猜想
DOI：
10.1093/imrn/rnz129
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发表时间：
2019
影响因子：
1
通讯作者：
Kurihara Masato
中科院分区：
文献类型：
--
作者：
Kim Chan-Ho;Kurihara Masato
本文研究了上椭圆曲线的割圆扩张的Selmer群在有限次扩张上的拟合理想。特别地，对于在奇素数具有良好(超奇异)约化的椭圆曲线，我们给出了类似于Mazur和Tate的“弱主要猜想”的一个证明。在主要猜想成立和某一误差项消失的情况下，证明了第二作者提出的“强主要猜想”。其核心思想是对岩泽理论中的“有限层对象”、“-对象”和“精细对象”进行明确的比较。对一般减法效果好的情况也作了处理。
In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic-extension ofof an elliptic curve over. Especially, we present a proof of the “weak main conjecture” à la Mazur and Tate for elliptic curves with good (supersingular) reduction at an odd prime. We also prove the “strong main conjecture” suggested by the second named author under the validity of the-main conjecture and the vanishing of a certain error term. The key idea is the explicit comparison among “finite layer objects”, “-objects”, and “fine objects” in Iwasawa theory. The case of good ordinary reduction is also treated.