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

DOI10.1016/J.JNT.2021.05.004arXiv2009.03772WikidataQ114156953 ScholiaQ114156953MaRDI QIDQ6348680

Antonio Lei, Jeffrey Hatley

Publication date: 8 September 2020

Abstract: We study the Selmer group associated to a $p$-ordinary newform $fin{S}_{2r}(Gamm{a}_0(N))$ over the anticyclotomic $mathbb{Z}_p$-extension of an imaginary quadratic field $K/mathbbQ$. 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.

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) (p)-adic theory, local fields (11F85) Holomorphic modular forms of integral weight (11F11) Iwasawa theory (11R23) Cyclotomic extensions (11R18)

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