Galois module structure of oriented Arakelov class groups

arXiv (Cornell University)

Abstract

We show that Chinburg's Omega(3) conjecture implies tight restrictions on the Galois module structure of oriented Arakelov class groups of number fields. We apply our findings to formulating a probabilistic model for Arakelov class groups in families, offering a correction of the Cohen--Lenstra--Martinet heuristics on ideal class groups.

Authors 3

1. Alex Bartel

   University of Glasgow

   Affiliation as printed

   *University of Glasgow

2. Henri Johnston

   University of Exeter

   Affiliation as printed

   The University of Exeter

3. Hendrik W. Lenstra Aachen

   Leiden University

   Affiliation as printed

   Leiden University