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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 (2020) Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions. Mathematical Proceedings of the Cambridge Philosophical Society. ISSN 1469-8064 (In Press)

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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
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:85677
Publisher:Cambridge University Press

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