Abstract:
This paper investigates the question of birational equivalence of linear algebraic groups. Certain necessary conditions are derived for rationality of a group over the field of definition, which in application to algebraic tori are fairly delicate. In particular, it is shown that the condition $\textrm{Ø}(G)=0$ is a necessary criterion of rationality for tori and for semisimple groups defined over an algebraic number field.
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