Weak approximation, Brauer and R-equivalence in algebraic groups over arithmetical fields
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 1997
- DOI:
- 10.48550/arXiv.alg-geom/9711015
- arXiv:
- arXiv:alg-geom/9711015
- Bibcode:
- 1997alg.geom.11015T
- Keywords:
-
- Algebraic Geometry;
- Mathematics - Algebraic Geometry
- E-Print:
- LaTeX 2e, 58 pages, revised and extended