论文标题
椭圆形曲线的伊瓦川理论
Equivariant Iwasawa theory for elliptic curves
论文作者
论文摘要
我们讨论了Abelian Equivariant iwasawa理论，以元素的质量和非异常的良好普通素数以$ \ mathbb {q} $上的椭圆曲线。使用Kobayashi的方法，我们构建了Equivariant Coleman Maps，该地图将Beilinson-Kato Element发送到Equivariant $ P $ -ADIC $ L $ functions。然后，我们提出了模棱两可的主要猜想，在某些假设下，通过Euler System机械证明了一种分裂性。作为一种应用，我们证明了一种猜想的Mazur-Tate案例。
We discuss abelian equivariant Iwasawa theory for elliptic curves over $\mathbb{Q}$ at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the Beilinson-Kato element to the equivariant $p$-adic $L$-functions. Then we propose equivariant main conjectures and, under certain assumptions, prove one divisibility via Euler system machinery. As an application, we prove a case of a conjecture of Mazur-Tate.
