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arXiv · 2107.06644

On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple $\mathbb{Z}_p$-Extensions Over Imaginary Quadratic Fields

Takashi Miura·Kazuaki Murakami·Keiji Okano·Rei Otsuki
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Abstract

For an odd prime number $p$, we study the number of generators of the unramified Iwasawa modules of the maximal multiple $\mathbb{Z}_p$-extensions over Iwasawa algebra. In a previous paper of the authors, under several assumptions for an imaginary quadratic field, we obtain a necessary and sufficient condition for the Iwasawa module to be cyclic as a module over the Iwasawa algebla. Our main result is to give methods for computation and numerical examples about the results. We remark that our results do not need the assumption that Greenberg's generalized conjecture holds.

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Takashi Miura, Kazuaki Murakami, Keiji Okano, Rei Otsuki. 2021-07-13. On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple $\mathbb{Z}_p$-Extensions Over Imaginary Quadratic Fields. https://arxiv.org/abs/2107.06644

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