Explicit methods for the Hasse norm principle and applications to A _n and S _n extensions

TY - JOUR

T1 - Explicit methods for the Hasse norm principle and applications to A n and S n extensions

AU - Macedo, André

AU - Newton, Rachel

N1 - Publisher Copyright: © The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus \[R_{K/k}^1{\mathbb{G}_m}\] . We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

AB - Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus \[R_{K/k}^1{\mathbb{G}_m}\] . We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

KW - 11E72

KW - 11R37

KW - 14G05

KW - 2020 Mathematics Subject Classification:

KW - 20G30

UR - https://www.scopus.com/pages/publications/85104773828

U2 - 10.1017/S0305004121000268

DO - 10.1017/S0305004121000268

M3 - Article

AN - SCOPUS:85104773828

SN - 0305-0041

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -