Work

Universal quadratic forms and Northcott property of infinite number fields

Year: 2024

Type: article

Abstract: We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals , then the set of totally positive integers in the extension does not have the Northcott property. In particular, this implies that no universal form exists over the compositum of all totally real Galois fields of a fixed prime degree over . Further, by considering the existence of infinitely many square classes of totally positive units, we show that no classical universal form exists over the compositum of all such fields of degree (for each fixed odd integer ).

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70022

Authors: Nicolas Daans, Vítězslav Kala, Siu Hang Man

Institution: Charles University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: Univerzita Karlova v Praze, Grantová Agentura České Republiky