On the Hida deformations of fine Selmer groups

In this paper, we study the fine Selmer group of p-adic Galois representations and their deformations. We show that for an infinite family of elliptic cuspforms, if the μ-invariant of the dual fine Selmer group is zero for one member of the family, then the same holds for all the other members. Further the λ-invariants are equal for all but finitely many members in the family.