Arakelov class groups of random number fields

arXiv (Cornell University)

Abstract

The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen--Lenstra--Martinet heuristic on ideal class groups. To that end, we show that Chinburg's Omega(3) conjecture implies tight restrictions on the Galois module structure of oriented Arakelov class groups. As a consequence, we construct a new infinite series of counterexamples to the Cohen--Lenstra--Martinet heuristic, which have the novel feature that their Galois groups are non-abelian.

Authors 3

1. Alex Bartel

   University of Glasgow

   Affiliation as printed

   School of Mathematics and Statistics , University of Glasgow , University Place , Glasgow G12 8SQ , United Kingdom

2. Henri Johnston

   University of Exeter

   Affiliation as printed

   Department of Mathematics and Statistics , University of Exeter , Exeter EX4 4QF , United Kingdom

3. Hendrik W. Lenstra Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut , Universiteit Leiden , Postbus 9512 , 2300 RA Lei- den, The Netherlands