The first level of $\mathbb{Z}_p$-extensions and compatibility of heuristics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913538228879360 |
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| author | Kundu, Debanjana Washington, Lawrence C. |
| author_facet | Kundu, Debanjana Washington, Lawrence C. |
| contents | 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 $λ$ equals 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The first level of $\mathbb{Z}_p$-extensions and compatibility of heuristics Kundu, Debanjana Washington, Lawrence C. Number Theory 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 $λ$ equals 1. |
| title | The first level of $\mathbb{Z}_p$-extensions and compatibility of heuristics |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.06193 |