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Some remarks on Kida’s formula when \(\mu \ne 0\)

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Abstract

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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Acknowledgements

The author like to thank John Coates for his interest and comments on the paper. He would also like to thank the anonymous referee for many useful comments and suggestions on the article. Some part of the research of this article was conducted when the author was visiting the National University of Singapore and the National Center for Theoretical Sciences in Taiwan, and he would like to acknowledge the hospitality and conducive working conditions provided by these institutes.

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  1. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, P.R. China

    Meng Fai Lim

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  1. Meng Fai Lim
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The author’s research is supported by the National Natural Science Foundation of China under Grant No. 11550110172 and Grant No. 11771164.

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Lim, M.F. Some remarks on Kida’s formula when \(\mu \ne 0\). Ramanujan J 55, 1127–1144 (2021). https://doi.org/10.1007/s11139-021-00393-z

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