Weak approximation, R-equivalence, and Whitehead groups

1997 ◽  
pp. 345-354 ◽  
Author(s):  
Nguyen Thang
Keyword(s):  
Weak Approximation ◽  
Whitehead Groups

scholarly journals Test groups for Whitehead groups

2012 ◽  
Vol 42 (6) ◽  
pp. 1863-1873
Author(s):  
Paul C. Eklof ◽  
László Fuchs ◽  
Saharon Shelah
Keyword(s):  
Whitehead Groups

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

2021 ◽  
pp. 1-41
Author(s):  
ANDRÉ MACEDO ◽  
RACHEL NEWTON
Keyword(s):  
Galois Group ◽  
Computational Methods ◽  
Number Fields ◽  
Normal Closure ◽  
Explicit Methods ◽  
Weak Approximation ◽  
Norm Principle ◽  
Theoretical Results

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 \[R_{K/k}^1{\mathbb{G}_m}\] . 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.

scholarly journals Failures of weak approximation in families

2016 ◽  
Vol 152 (7) ◽  
pp. 1435-1475 ◽  
Author(s):  
M. J. Bright ◽  
T. D. Browning ◽  
D. Loughran
Keyword(s):  
Number Field ◽  
Weak Approximation

Given a family of varieties$X\rightarrow \mathbb{P}^{n}$over a number field, we determine conditions under which there is a Brauer–Manin obstruction to weak approximation for 100% of the fibres which are everywhere locally soluble.

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