Weak approximation, Brauer and Requivalence in algebraic groups over arithmetical fields
Abstract
We prove some new relations between weak approximation and some rational equivalence relations (Brauer and Requivalence) in algebraic groups over arithmetical fields. By using weak approximation and local  global approach, we compute completely the group of Brauer equivalence classes of connected linear algebraic groups over number fields, and also completely compute the group of Requivalence classes of connected linear algebraic groups $G$, which either are defined over a totally imaginary number field, or contains no anisotropic almost simple factors of exceptional type $^{3,6}\D_4$, nor $\E_6$. We discuss some consequences derived from these, e.g., by giving some new criteria for weak approximation in algebraic groups over number fields, by indicating a new way to give examples of non stably rational algebraic groups over local fields and application to norm principle.
 Publication:

arXiv eprints
 Pub Date:
 November 1997
 DOI:
 10.48550/arXiv.alggeom/9711015
 arXiv:
 arXiv:alggeom/9711015
 Bibcode:
 1997alg.geom.11015T
 Keywords:

 Algebraic Geometry;
 Mathematics  Algebraic Geometry
 EPrint:
 LaTeX 2e, 58 pages, revised and extended