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arXiv · 2009.03772

Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II

Jeffrey Hatley·Antonio Lei
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Abstract

We study the Selmer group associated to a $p$-ordinary newform $f \in S_{2r}(\Gamma_0(N))$ over the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K/\mathbb{Q}$. Under certain assumptions, we prove that this Selmer group has no proper $\Lambda$-submodules of finite index. This generalizes work of Bertolini in the elliptic curve case. We also offer both a correction and an improvement to an earlier result on Iwasawa invariants of congruent modular forms by the present authors.

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Jeffrey Hatley, Antonio Lei. 2020-09-08. Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II. https://doi.org/10.1016/j.jnt.2021.05.004

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