On class groups of random number fields

Abstract

The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics. We conclude by proposing a rigorously formulated Cohen--Lenstra--Martinet conjecture.

arXiv commentExpanded introduction, and other minor improvements in the exposition, 31 pages. Final version, to appear in Proc. London Math. Soc

References in corpus (2)

• On the probabilities of local behaviors in abelian field extensions
• Commensurability of automorphism groups

Cited by in corpus (5)

• Invariant part of class group and distribution of relative class group
• Counting integral points on symmetric varieties with applications to arithmetic statistics
• Malle's conjecture for fair counting functions
• Class number for pseudo-Anosovs
• Monogenicity and 2-torsion in the class group of number fields of odd degree