Most totally real fields do not have universal forms or the Northcott property
N
Nicolas Daans
V
Vítězslav Kala
(Department of Algebra)
S
Siu Hang Man
(Department of Algebra)
M
Martin Widmer
(Institute of Analysis and Number Theory)
P
Pavlo Yatsyna
(Department of Algebra)
Abstract
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 theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.
Article Details
Volume / Issue
Vol. 122, Issue 20
Published
May 20, 2025
ISSN
0027-8424
Publisher
National Academy of Sciences
Journal Info
Proceedings of the National Academy of Sciences
National Academy of Sciences
ISSN: 0027-8424 Life Sciences
Authors (5)
N
Nicolas Daans
V
Vítězslav Kala
Department of Algebra
S
Siu Hang Man
Department of Algebra
M
Martin Widmer
Institute of Analysis and Number Theory
P
Pavlo Yatsyna
Department of Algebra
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