### Weak approximation, Brauer and R-equivalence in algebraic groups over arithmetical fields, by Nguyen Quoc Thang

We prove some new relations between weak approximation
and some rational equivalence relations
(Brauer and R-equivalence) 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 R-equivalence 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.
This is a revision with extension of our previous paper.

Nguyen Quoc Thang <nguyen@tx.technion.ac.il>