Most totally real fields do not have universal forms or Northcott property

Most totally real fields do not have universal forms or Northcott property

We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by...

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Hauptverfasser: Daans, Nicolas, Kala, Vitezslav, Man, Siu Hang, Widmer, Martin, Yatsyna, Pavlo
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Number Theory
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Beschreibung
Zusammenfassung:We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.
DOI:10.48550/arxiv.2409.11082