On the distribution of \Cl(K)[l^\∞] for degree l cyclic\n fields

2018/12/17 by Peter Koymans, Carlo Pagano, Koymans, Peter +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1812.06884

openalex publication_date 2018/12/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Using a recent breakthrough of Alexander Smith, we prove that\nl^\∞-class groups of cyclic degree l fields have the distribution\nconjectured by Gerth under GRH.\n

Related

• Distribution of the bad part of class groups
• 2^∞-Selmer groups, 2^∞-class groups, and Goldfeld's conjecture
• The distribution of ℓ^∞-Selmer groups in degree ℓ twist families I
• The distribution of ℓ^∞-Selmer groups in degree ℓ twist families II
• On the mu and lambda invariants of the logarithmic class group