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arXiv · 2410.06193

The first level of $\mathbb{Z}_p$-extensions and compatibility of heuristics

Debanjana Kundu·Lawrence C. Washington
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Abstract

Let $K$ be an imaginary quadratic field in which the odd prime $p$ does not split. When the $p$-part of the class group of $K$ is cyclic, we describe the possible structures for the $p$-part of the class group of the first level of the cyclotomic $\mathbb{Z}_p$-extension of $K$. This allows us to show the compatibility of the heuristics of Cohen--Lenstra--Martinet for class groups with the heuristics of Ellenberg--Jain--Venkatesh for how often the cyclotomic Iwasawa invariant $\lambda$ equals 1.

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Debanjana Kundu, Lawrence C. Washington. 2024-10-08. The first level of $\mathbb{Z}_p$-extensions and compatibility of heuristics. https://arxiv.org/abs/2410.06193

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