On the corank of the fine Selmer group of an elliptic curve over a $\mathbb{Z}_p$-extension

Anwesh Ray

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arXiv · 2208.13247

On the corank of the fine Selmer group of an elliptic curve over a $\mathbb{Z}_p$-extension

Anwesh Ray

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Abstract

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 $\lambda$-invariant), in terms of various local and global invariants.

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Anwesh Ray. 2022-08-28. On the corank of the fine Selmer group of an elliptic curve over a $\mathbb{Z}_p$-extension. https://arxiv.org/abs/2208.13247

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