Some remarks on Kida's formula when $μ\neq 0$

英文摘要：

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