Fine Selmer groups of congruent <i>p</i>-adic Galois representations

We compare the Pontryagin duals of fine Selmer groups two congruent $p$-adic Galois representations over admissible pro-$p$, Lie extensions $K_\infty$ number fields $K$. prove that in several natural settings $\pi$-primary submodules are pseudo-isomorphic Iwasawa algebra; if coranks not equal, then we can still inequalities between $\mu$-invariants. In special case a $\mathbb{Z}_p$-extension $K_\infty/K$, also $\lambda$-invariants groups, even situations where $\mu$-invariants non-zero. Finally, similar results for certain abelian non-$p$-extensions.