On class groups of random number fields

Bartel, Alex; Lenstra, Hendrik W.

doi:10.1112/plms.12343

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学術論文

On class groups of random number fields

MPS-Authors

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Bartel, Alex
Max Planck Institute for Mathematics, Max Planck Society;

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Lenstra, Hendrik W.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/plms.12343
(出版社版)

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Bartel-Lenstra_On class groups of random number fields_2020.pdf
(出版社版), 412KB

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引用

Bartel, A., & Lenstra, H. W. (2020). On class groups of random number fields. Proceedings of the London Mathematical Society, 121(4), 927-953. doi:10.1112/plms.12343.

引用: https://hdl.handle.net/21.11116/0000-0006-95B4-6

要旨

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.