On the Northcott property for infinite extensions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929196110970880 |
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| author | Widmer, Martin |
| author_facet | Widmer, Martin |
| contents | We start with a brief survey on the Northcott property for subfields of the algebraic numbers $\Qbar$. Then we introduce a new criterion for its validity (refining the author's previous criterion), addressing a problem of Bombieri. We show that Bombieri and Zannier's theorem, stating that the maximal abelian extension of a number field $K$ contained in $K^{(d)}$ has the Northcott property, follows very easily from this refined criterion. Here $K^{(d)}$ denotes the composite field of all extensions of $K$ of degree at most $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Northcott property for infinite extensions Widmer, Martin Number Theory Primary 11R04, 11G50 Secondary 11R06, 11R20, 37P30 We start with a brief survey on the Northcott property for subfields of the algebraic numbers $\Qbar$. Then we introduce a new criterion for its validity (refining the author's previous criterion), addressing a problem of Bombieri. We show that Bombieri and Zannier's theorem, stating that the maximal abelian extension of a number field $K$ contained in $K^{(d)}$ has the Northcott property, follows very easily from this refined criterion. Here $K^{(d)}$ denotes the composite field of all extensions of $K$ of degree at most $d$. |
| title | On the Northcott property for infinite extensions |
| topic | Number Theory Primary 11R04, 11G50 Secondary 11R06, 11R20, 37P30 |
| url | https://arxiv.org/abs/2310.11337 |