论文标题
在$ \ mathbb {z} _p $ - extension上的椭圆曲线的精细Selmer组的核心上
On the corank of the fine Selmer group of an elliptic curve over a $\mathbb{Z}_p$-extension
论文作者
论文摘要
令$ p $为奇数，$ f_ \ infty $为$ \ mathbb {z} _p $ - 数字字段$ f $的扩展。鉴于椭圆曲线$ e $ $ $ f $，我们研究了$ f_ \ infty $的优质Selmer组的结构。结果表明，在某些条件下，精细的Selmer组是一个超过$ \ Mathbb {Z} _p $的可加工的模块，此外，我们在各种本地和全球不可投射的方面都获得了其Corank的上限（即$λ$ -Invariant）。
Let $p$ be an odd prime and $F_\infty$ be a $\mathbb{Z}_p$-extension of a number field $F$. Given an elliptic curve $E$ over $F$, we study the structure of the fine Selmer group over $F_\infty$. It is shown that under certain conditions, the fine Selmer group is a cofinitely generated module over $\mathbb{Z}_p$ and furthermore, we obtain an upper bound for its corank (i.e., the $λ$-invariant), in terms of various local and global invariants.
