Arakelov class groups of random number fields
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866909152981286912 |
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| author | Bartel, Alex Johnston, Henri Lenstra Jr, Hendrik W. |
| author_facet | Bartel, Alex Johnston, Henri Lenstra Jr, Hendrik W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_11533 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Arakelov class groups of random number fields Bartel, Alex Johnston, Henri Lenstra Jr, Hendrik W. Number Theory 11R29, 11R33, 11R65 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. |
| title | Arakelov class groups of random number fields |
| topic | Number Theory 11R29, 11R33, 11R65 |
| url | https://arxiv.org/abs/2005.11533 |