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

André Macedo, Rachel Newton

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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 <![CDATA[ \[R_{K/k}^1{\mathbb{G}_m}\] ]]>. 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.

Original languageEnglish
JournalMathematical Proceedings of the Cambridge Philosophical Society
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • 11E72
  • 11R37
  • 14G05
  • 2020 Mathematics Subject Classification:
  • 20G30

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