On the distribution of ${Cl}(K)[l^\infty]$ for degree $l$ cyclic fields

Peter Koymans; Carlo Pagano

doi:10.4171/jems/1112

JournalsjemsVol. 24, No. 4pp. 1189–1283

On the distribution of $Cl (K) [l^{\infty}]$ for degree $l$ cyclic fields

Peter Koymans
Leiden University, Netherlands
Carlo Pagano
Max Planck Institute for Mathematics, Bonn, Germany

$On the distribution of ${Cl}(K)[l^\infty]$ for degree $l$ cyclic fields cover$

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Abstract

Using a recent breakthrough of Smith [22], we prove that $l^{\infty}$ -class groups of cyclic degree $l$ fields have the distribution conjectured by Gerth under GRH.

Cite this article

Peter Koymans, Carlo Pagano, On the distribution of $Cl (K) [l^{\infty}]$ for degree $l$ cyclic fields. J. Eur. Math. Soc. 24 (2022), no. 4, pp. 1189–1283

DOI 10.4171/JEMS/1112