Faithful Artin induction and the Chebotarev density theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909201602707456 |
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| author | Oliver, Robert J. Lemke Smith, Alexander |
| author_facet | Oliver, Robert J. Lemke Smith, Alexander |
| contents | Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number field F, almost all are subject to a strong effective version of the Chebotarev density theorem. We use this version of the Chebotarev density theorem to deduce several consequences for class groups in families of number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Faithful Artin induction and the Chebotarev density theorem Oliver, Robert J. Lemke Smith, Alexander Number Theory Group Theory Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number field F, almost all are subject to a strong effective version of the Chebotarev density theorem. We use this version of the Chebotarev density theorem to deduce several consequences for class groups in families of number fields. |
| title | Faithful Artin induction and the Chebotarev density theorem |
| topic | Number Theory Group Theory |
| url | https://arxiv.org/abs/2405.08383 |