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 $f\in S_{2r}({\Gamma }_0(N))$ 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.

arXiv commentTo appear in Journal of Number Theory

References in corpus (9)

• Variation of Iwasawa invariants in Hida families
• On the Iwasawa invariants of elliptic curves
• On the anticyclotomic Iwasawa main conjecture for modular forms
• On the non-triviality of the $p$-adic Abel-Jacobi image of generalised Heegner cycles modulo $p$, II: Shimura curves
• Kolyvagin systems and Iwasawa theory of generalized Heegner cycles
• $p$-adic heights of Heegner points and Beilinson-Flach elements
• Congruences between Heegner points and quadratic twists of elliptic curves
• Arithmetic properties of signed Selmer groups at non-ordinary primes
• $\Lambda$-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves

Cited by in corpus (4)

• Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves
• On fine Selmer groups and the greatest common divisor of signed and chromatic $p$-adic $L$-functions
• On the cohomology of plus/minus Selmer groups of supersingular elliptic curves in weakly ramified base fields
• The vanishing of anticyclotomic $\mu$-invariants for non-ordinary modular forms