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.

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$$ \ mu \ ne 0 $$μ≠0时对Kida公式的一些评论

经典Iwasawa理论中的Kida公式与Iwasawa \（\ lambda \） - p-数域扩展的不变量相关。随后在适当的\（\ mu = 0 \）假设下，为Selmer组的Iwasawa \（\ lambda \）-不变量建立了该公式的类似物。在本文中，我们给出了一个概念性（但推测性的）解释，即当\（\ mu \ ne 0 \）时，该公式也应成立。猜想成分来自非交换Iwasawa理论中的\（{\ mathfrak {M}} _ H（G）\）-猜想。