Number fields with prescribed norms: with an appendix by Y. Harpaz and O. Wittenberg

Christopher Frei; Daniel Loughran; Rachel Newton

doi:10.4171/CMH/528

Number fields with prescribed norms: with an appendix by Y. Harpaz and O. Wittenberg

Christopher Frei, Daniel Loughran^*, Rachel Newton

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We study the distribution of extensions of a number field k with fixed abelian Galois group G, from which a given finite set of elements of k are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for 100% of G-extensions of k, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result.

Original language	English
Pages (from-to)	138-181
Number of pages	44
Journal	Commentarii Mathematici Helvetici
Volume	97
Issue number	1
DOIs	https://doi.org/10.4171/CMH/528
Publication status	Published - 2022

Keywords

class field theory
harmonic analysis
Hasse norm principle
rational points on varieties

ASJC Scopus subject areas

Mathematics(all)

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10.4171/CMH/528Licence: CC BY 4.0

https://arxiv.org/pdf/1810.06024.pdf

Cite this

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KW - rational points on varieties

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Number fields with prescribed norms: with an appendix by Y. Harpaz and O. Wittenberg

Abstract

Keywords

ASJC Scopus subject areas

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