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arXiv · 2108.06656

On fine Selmer groups and signed Selmer groups of elliptic modular forms

Antonio Lei·Meng Fai Lim
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Abstract

Let $f$ be an elliptic modular form and $p$ an odd prime that is coprime to the level of $f$. We study the link between divisors of the characteristic ideal of the $p$-primary fine Selmer group of $f$ over the cyclotomic $\mathbb{Z}_p$ extension of $\mathbb{Q}$ and the greatest common divisor of signed Selmer groups attached to $f$ defined using the theory of Wach modules. One of the key ingredients of our proof is a generalization of a result of Wingberg on the structure of fine Selmer groups of abelian varieties with supersingular reduction at $p$ to the context of modular forms.

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Antonio Lei, Meng Fai Lim. 2021-08-15. On fine Selmer groups and signed Selmer groups of elliptic modular forms. https://doi.org/10.1017/s0004972721000976

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