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arXiv · 2003.06546

On $p$-class groups of relative cyclic $p$-extensions

Yasushi Mizusawa·Kota Yamamoto
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Abstract

We prove a general stability theorem for $p$-class groups of number fields along relative cyclic extensions of degree $p^2$, which is a generalization of a finite-extension version of Fukuda's theorem by Li, Ouyang, Xu and Zhang. As an application, we give an example of pseudo-null Iwasawa module over a certain $2$-adic Lie extension.

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Yasushi Mizusawa, Kota Yamamoto. 2020-03-14. On $p$-class groups of relative cyclic $p$-extensions. https://doi.org/10.1007/s00013-021-01619-8

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