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arXiv · 2309.03745

Asymptotic growth patterns for class field towers

Arindam Bhattacharyya·Vishnu Kadiri·Anwesh Ray
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Abstract

Let $p$ be an odd prime number. We study growth patterns associated with finitely ramified Galois groups considered over the various number fields varying in a $\mathbb{Z}_p$-tower. These Galois groups can be considered as non-commutative analogues of ray class groups. For certain $\mathbb{Z}_p$-extensions in which a given prime above $p$ is completely split, we prove precise asymptotic lower bounds. Our investigations are motivated by the classical results of Iwasawa, who showed that there are growth patterns for $p$-primary class numbers of the number fields in a $\mathbb{Z}_p$-tower.

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BibTeXRIS

Arindam Bhattacharyya, Vishnu Kadiri, Anwesh Ray. 2023-09-07. Asymptotic growth patterns for class field towers. https://doi.org/10.4171/dm%2F949

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