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arXiv · 2005.11533

Arakelov class groups of random number fields

Alex Bartel·Henri Johnston·Hendrik W. Lenstra Jr
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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.

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Alex Bartel, Henri Johnston, Hendrik W. Lenstra Jr. 2020-05-23. Arakelov class groups of random number fields. https://arxiv.org/abs/2005.11533

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