Universal quadratic forms and Northcott property of infinite number fields

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489841" target="_blank" >RIV/00216208:11320/24:10489841 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KtGj1EzxrV" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KtGj1EzxrV</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.70022" target="_blank" >10.1112/jlms.70022</a>

Result language
angličtina
Original language name
Universal quadratic forms and Northcott property of infinite number fields
Original language description
We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals Q$mathbb {Q}$, 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 Q$mathbb {Q}$. 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 3d$3d$ (for each fixed odd integer d$d$).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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