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

[摘要] We study the Selmer group associated to a p-ordinary newform f is an element of S-2r(Gamma(0)(N)) over the anticyclotomic Z(p)-extension of an imaginary quadratic field K/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. Along the way, we prove a general result on the vanishing of several anticyclotomic mu-invariants attached to f. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Anticyclotomic extensions;Selmer groups;Modular forms;Congruences