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.

To 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
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• Arithmetic properties of signed Selmer groups at non-ordinary primes
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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