Some remarks on Kida's formula when $\mu \ne 0$

Abstract

The Kida's formula in classical Iwasawa theory relates the Iwasawa $\lambda$-invariants of $p$-extensions of number fields. Analogue of this formula was subsequently established for the Iwasawa $\lambda$-invariants of Selmer groups under an appropriate $\mu =0$ assumption. In this paper, we give a conceptual (but conjectural) explanation that such a formula should also hold when $\mu \ne 0$. The conjectural component comes from the so-called ${\mathfrak{M}}_H(G)$-conjecture in noncommutative Iwasawa theory.

arXiv comment16 pages

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Cited by in corpus (1)

• Asymptotic growth of Mordell-Weil ranks of elliptic curves in noncommutative towers