Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions

Macedo, A. and Newton, R. ORCID: https://orcid.org/0000-0003-4925-635X (2022) Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions. Mathematical Proceedings of the Cambridge Philosophical Society, 172 (3). pp. 489-529. ISSN 1469-8064 doi: 10.1017/S0305004121000268

Abstract/Summary

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^1_{K/k}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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/85677
Identification Number/DOI	10.1017/S0305004121000268
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Cambridge University Press
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