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Number fields without universal quadratic forms of small rank exist in most degrees

Part of: Forms and linear algebraic groups Algebraic number theory: global fields

Published online by Cambridge University Press:  06 May 2022

VÍTĚZSLAV KALA
VÍTĚZSLAV KALA*
Affiliation:
Charles University, Faculty of Mathematics and Physics, Department of Algebra, Sokolovská 49/83, 18675 Praha 8, Czech Republic. e-mails: kala@karlin.mff.cuni.cz, vita.kala@gmail.com
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Abstract

We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.

MSC classification

Primary: 11E12: Quadratic forms over global rings and fields
Secondary: 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 11R21: Other number fields 11R80: Totally real fields
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 2 , March 2023 , pp. 225 - 231
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

†

The author was supported by Czech Science Foundation GAČR, grant 21-00420M, and by Charles University, projects PRIMUS/20/SCI/002 and UNCE/SCI/022.

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