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

André Macedo; Rachel Newton

doi:10.1017/S0305004121000268

Explicit methods for the Hasse norm principle and applications to A _nand S _nextensions

André Macedo, Rachel Newton

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (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 language	English
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
DOIs	https://doi.org/10.1017/S0305004121000268
Publication status	Accepted/In press - 2021

Keywords

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

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10.1017/S0305004121000268

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title = "Explicit methods for the Hasse norm principle and applications to A n and S n extensions",

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. ",

keywords = "11E72, 11R37, 14G05, 2020 Mathematics Subject Classification:, 20G30",

author = "Andr{\'e} Macedo and Rachel Newton",

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year = "2021",

doi = "10.1017/S0305004121000268",

language = "English",

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AU - Newton, Rachel

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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 <![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.

KW - 11E72

KW - 11R37

KW - 14G05

KW - 2020 Mathematics Subject Classification:

KW - 20G30

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JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -

Explicit methods for the Hasse norm principle and applications to A _nand S _nextensions

Abstract

Keywords

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