Fine Selmer groups of modular forms

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 GK of K , and choose a GK -invariant lattice T ⊆ V . We study the fine Selmer groups of A = V/T over suitable p -adic Lie extensions K_∞ /K , comparing their corank and μ -invariant to the corank and the μ -invariant of the Iwasawa module of ideal class groups in K_∞ /K . In the second part of the article, we compare the Iwasawa μ - and l₀ -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 Zₚ -extensions of K .