We compare the Iwasawa invariants of fine Selmer groups of p-adic Galois representations over admissible p-adic Lie extensions of a number field K to the Iwasawa invariants of ideal class groups along these Lie extensions. More precisely, let K be a number field, let V be a p-adic representation of the absolute Galois group \(G_K\) of K, and choose a \(G_K\) -invariant lattice \({T \subseteq V}\) . We study the fine Selmer groups of \({A = V/T}\) over suitable p-adic Lie extensions \(K_\infty /K\) , comparing their corank and \(\mu \) -invariant to the corank and the \(\mu \) -invariant of the Iwasawa module of ideal class groups in \(K_\infty /K\) . In the second part of the article, we compare the Iwasawa \(\mu \) - and \(l_0\) -invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple \(\mathbb {Z}_p\) -extensions of K.
