PreprintCC BY 4.0arXiv
p-class groups in the cyclotomic ℤp-extension of imaginary quadratic fields
Abstract
We study the structure of the p-class group of the first layer of the cyclotomic ℤp-extension of an imaginary quadratic field where p is non-split. We obtain restrictions on the growth of the cyclic factors from the base layer to the first layer; in particular, when the p-rank remains unchanged, each cyclic factor grows by exactly one power of p. We show that in a large number of cases the Iwasawa λ-invariant is completely determined by the p-rank of the first layer itself. Finally we use a Cohen-Lenstra-Martinet type philosophy to study the probability distribution of Iwasawa lambda invariants of the first layer when the base layer has cyclic p-class group.
Related
- Mild p-Class Tower Groups of Imaginary Quadratic Fields
- Maximal unramified 3-extensions of imaginary quadratic fields and \textrm SL\sb 2(\mathbb Z\sb 3)
- Automorphic symbols and automorphic \emph{L}-values of GL(2) over imaginary quadratic fields
- The enhanced polylogarithm conjecture in weight two for imaginary quadratic fields
- Bowen--Franks groups and minus class groups of imaginary abelian fields
BibTeX
@misc{jha2026pclass,
title = {{$p$-class groups in the cyclotomic $\mathbbZ_p$-extension of imaginary quadratic fields}},
author = {Somnath Jha and Debanjana Kundu and H. Laxmi and Lawrence C. Washington},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10452},
eprint = {2610.10452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10452},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - p-class groups in the cyclotomic ℤ_p-extension of imaginary quadratic fields
AU - Somnath Jha
AU - Debanjana Kundu
AU - H. Laxmi
AU - Lawrence C. Washington
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10452
UR - https://arxiv.org/abs/2610.10452
AB - We study the structure of the p-class group of the first layer of the cyclotomic ℤ_p-extension of an imaginary quadratic field where p is non-split. We obtain restrictions on the growth of the cyclic factors from the base layer to the first layer; in particular, when the p-rank remains unchanged, each cyclic factor grows by exactly one power of p. We show that in a large number of cases the Iwasawa λ-invariant is completely determined by the p-rank of the first layer itself. Finally we use a Cohen-Lenstra-Martinet type philosophy to study the probability distribution of Iwasawa lambda invariants of the first layer when the base layer has cyclic p-class group.
ER -