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

Abstract

We study the Selmer group associated to a p-ordinary newform f∈S2r(Γ0(N)) over the anticyclotomic Zp-extension of an imaginary quadratic field K/Q. Under certain assumptions, we prove that this Selmer group has no proper Λ-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 μ-invariants attached to f.