We consider a generalization of a result of Kida in classical Iwasawa theory which relates Iwasawa invariants of $p$-extensions of number fields. In this paper, we consider Selmer groups of a general class of Galois representations which includes the case of $p$-ordinary Hilbert modular forms and $p$-supersingular modular forms.

11R23, 11R20, 11R21, 11S40, 11F80

Iwasawa theory, abelian extensions, other number fields, $p$-adic $L$-functions, Galois representations