Field change for the Cassels-Tate pairing and applications to class groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866915535963291648 |
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| author | Morgan, Adam Smith, Alexander |
| author_facet | Morgan, Adam Smith, Alexander |
| contents | In previous work, the authors defined a category $SMod_F$ of finite Galois modules decorated with local conditions for each global field $F$. In this paper, given an extension $K/F$ of global fields, we define a restriction of scalars functor from $SMod_K$ to $SMod_F$ and show that it behaves well with respect to the Cassels-Tate pairing. We apply this work to study the class groups of global fields in the context of the Cohen-Lenstra heuristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13403 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Field change for the Cassels-Tate pairing and applications to class groups Morgan, Adam Smith, Alexander Number Theory 11R34 (11R29, 11R37) In previous work, the authors defined a category $SMod_F$ of finite Galois modules decorated with local conditions for each global field $F$. In this paper, given an extension $K/F$ of global fields, we define a restriction of scalars functor from $SMod_K$ to $SMod_F$ and show that it behaves well with respect to the Cassels-Tate pairing. We apply this work to study the class groups of global fields in the context of the Cohen-Lenstra heuristics. |
| title | Field change for the Cassels-Tate pairing and applications to class groups |
| topic | Number Theory 11R34 (11R29, 11R37) |
| url | https://arxiv.org/abs/2206.13403 |