Explicit methods for the Hasse norm principle and applications toAnandSnextensions

DOI10.1017/S0305004121000268MaRDI QIDQ5087126

André Macedo, Rachel Newton

Publication date: 8 July 2022

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.03730

zbMATH Keywords

weak approximationHasse norm principle

Mathematics Subject Classification ID

Rational points (14G05) Linear algebraic groups over global fields and their integers (20G30) Class field theory (11R37) Galois cohomology of linear algebraic groups (11E72) Hasse principle, weak and strong approximation, Brauer-Manin obstruction (14G12)

Related Items (1)

Norm one Tori and Hasse norm principle

Uses Software

• GAP
• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Davenport-Heilbronn theorems and second order terms
• On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields
• The density of discriminants of quintic rings and fields
• Maximal tori without effect in semisimple algebraic groups
• Principal homogeneous spaces under flasque tori; applications
• The admissibility of \(A_5\)
• Zur Arithmetik von Diedergruppenerweiterungen
• Zur Arithmetik von Konjugationsklassen in algebraischen Gruppen
• \(\mathbb Q\)-admissibility questions for alternating groups
• The Magma algebra system. I: The user language
• Equality of norm groups of subextensions of \(S_ n\) \((n\leq 5)\) extensions of algebraic number fields.
• On \(\ell\)-torsion in class groups of number fields
• Nonabelian Cohen-Lenstra moments
• Odd degree number fields with odd class number
• Formulas for the unramified Brauer group of a principal homogeneous space of a linear algebraic group.
• The number of \(D_4\)-fields ordered by conductor
• Number fields with prescribed norms (with an appendix by Yonatan Harpaz and Olivier Wittenberg)
• An effective Chebotarev density theorem for families of number fields, with an application to \(\ell \)-torsion in class groups
• The Hasse norm principle for \(A_n\)-extensions
• Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions
• The density of discriminants of quartic rings and fields
• The number of extensions of a number field with fixed degree and bounded discriminant
• Subfields of division rings. I
• Unramified extensions of quadratic number fields. II
• THE HASSE NORM PRINCIPLE FOR ALGEBRAIC NUMBER FIELDS
• Density of discriminants of cubic extensions.
• On the complete obstruction to the Hasse principle
• La $R$-équivalence sur les tores
• On the Hasse norm principle.
• The Hasse norm principle in non-abelian extensions.
• The Hasse norm principle for abelian extensions
• How often does the Hasse principle hold?
• The Hasse Norm Principle For Biquadratic Extensions
• Rationality Problem for Algebraic Tori
• BIRATIONAL PROPERTIES OF LINEAR ALGEBRAIC GROUPS
• Focal Series in Finite Groups
• On the distribution of Galois groups

This page was built for publication: Explicit methods for the Hasse norm principle and applications toA_nandS_nextensions