论文标题
全球领域的精美Selmer群体理论
Iwasawa theory of fine Selmer groups over global fields
论文作者
论文摘要
$ p^\ infty $ -fine selmer组的椭圆曲线$ e $ a $ f $ f $是经典$ p^\ infty $ -selmer $ e $ $ e $ y $ f $的子组。 Fine Selmer组与第一和第二个伊瓦沙瓦人的共同学组密切相关。 Coates-Sujatha观察到，在$ p $ - ad-adic lie lie的扩展上，数字字段的$ e $ $ e $的结构与古典iwasawa理论中的一些深度问题相关。例如，伊瓦沙（Iwasawa）的古典$μ$ $ invariant消失的猜想。在本文中，我们研究了$ p^\ infty $ fine selmer组的椭圆形曲线组的属性，该曲线是一个数字字段的某些$ p $ - 亚种式的扩展。我们还定义并讨论了椭圆形曲线的$ p^\ infty $ - 固定曲线，这些椭圆形曲线是特征性$ p $的功能字段，以及特征性$ \ ell \ neq p。$，我们将我们的研究与Jannsen的猜想联系起来。
The $p^\infty$-fine Selmer group of an elliptic curve $E$ over a number field $F$ is a subgroup of the classical $p^\infty$-Selmer group of $E$ over $F$. Fine Selmer group is closely related to the 1st and 2nd Iwasawa cohomology groups. Coates-Sujatha observed that the structure of the fine Selmer group of $E$ over a $p$-adic Lie extension of a number field is intricately related to some deep questions in classical Iwasawa theory; for example, Iwasawa's classical $μ$-invariant vanishing conjecture. In this article, we study the properties of the $p^\infty$-fine Selmer group of an elliptic curve over certain $p$-adic Lie extensions of a number field. We also define and discuss $p^\infty$-fine Selmer group of an elliptic curve over function fields of characteristic $p$ and also of characteristic $\ell \neq p.$ We relate our study with a conjecture of Jannsen.
