arXiv Open Access 2024

On Widmer's criteria for the Northcott property

Sara Checcoli Arno Fehm

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Abstrak

Recently, Widmer introduced a new sufficient criterion for the Northcott property on the finiteness of elements of bounded height in infinite algebraic extensions of number fields. We provide a simplification of Widmer's criterion when the extension is abelian, and use this to exhibit fields with the Northcott property that do not satisfy Widmer's new criterion. We also show how the construction of pseudo algebraically closed fields with the Northcott property, carried out in previous work using the first version of Widmer's criterion, can be simplified.

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math.NT

Penulis (2)

Sara Checcoli

Arno Fehm

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Checcoli, S., Fehm, A. (2024). On Widmer's criteria for the Northcott property. https://arxiv.org/abs/2401.03730

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Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓