Kida's Formula and Congruences

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.

2000 Mathematics Subject Classification: 11R23

Keywords and Phrases: Iwasawa theory, Kida's formula

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