Abstract
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.
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