References & Citations
Mathematics > Number Theory
Title: Arakelov class groups of random number fields
(Submitted on 23 May 2020 (v1), last revised 27 Mar 2024 (this version, v3))
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.
Submission history
From: Alex Bartel [view email][v1] Sat, 23 May 2020 13:16:12 GMT (18kb)
[v2] Tue, 27 Sep 2022 13:07:17 GMT (31kb)
[v3] Wed, 27 Mar 2024 16:43:37 GMT (26kb)
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