TY - JOUR
T1 - Number fields with prescribed norms
T2 - with an appendix by Y. Harpaz and O. Wittenberg
AU - Frei, Christopher
AU - Loughran, Daniel
AU - Newton, Rachel
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - class field theory
KW - harmonic analysis
KW - Hasse norm principle
KW - rational points on varieties
UR - http://www.scopus.com/inward/record.url?scp=85130937980&partnerID=8YFLogxK
U2 - 10.4171/CMH/528
DO - 10.4171/CMH/528
M3 - Article
SN - 0010-2571
VL - 97
SP - 138
EP - 181
JO - Commentarii Mathematici Helvetici
JF - Commentarii Mathematici Helvetici
IS - 1
ER -