论文标题
猜想A和$ $ $ invariant用于Selmer selmer superingular椭圆曲线
Conjecture A and $μ$-invariant for Selmer groups of supersingular elliptic curves
论文作者
论文摘要
让$ p $是一个奇怪的素数，让$ e $为椭圆曲线定义在数字$ f $上，在$ p $以上的素数减少。在这篇调查文章中，我们概述了精美的Selmer组和签名的Selmer团体在循环塔上证明的一些重要结果，以及在$ \ Mathbb {z} _p^2 $ extensions of Cyclotomic Towers以及签名的Selmer组上，其中一个虚构的Quadratic Quadratic fiepentions of $ p $ p $ splits完全完全。我们仅通过伊瓦沙理论讨论这些对象的代数方面。我们还试图给出一些最近的结果，这意味着在猜想的假设中消失了$ $ $ invariant A。我们重点介绍了签名的Selmer群体的特性（当$ E $具有良好的超级减少时），这完全类似于古典Selmer组（当$ E $具有良好的普通降低时）。在本调查文件中，我们没有提供任何证据，但是我们试图为有兴趣的读者提供讨论结果的参考。
Let $p$ be an odd prime and let $E$ be an elliptic curve defined over a number field $F$ with good reduction at primes above $p$. In this survey article, we give an overview of some of the important results proven for the fine Selmer group and the signed Selmer groups over cyclotomic towers as well as the signed Selmer groups over $\mathbb{Z}_p^2$-extensions of an imaginary quadratic field where $p$ splits completely. We only discuss the algebraic aspects of these objects through Iwasawa theory. We also attempt to give some of the recent results implying the vanishing of the $μ$-invariant under the hypothesis of Conjecture A. Moreover, we draw an analogy between the classical Selmer group in the ordinary reduction case and that of the signed Selmer groups of Kobayashi in the supersingular reduction case. We highlight properties of signed Selmer groups (when $E$ has good supersingular reduction) which are completely analogous to the classical Selmer group (when $E$ has good ordinary reduction). In this survey paper, we do not present any proofs, however we have tried to give references of the discussed results for the interested reader.
