This is an expanded version of my talk given at the International Conference``Algebra and
Number Theory''dedicated to the 80th anniversary of VE Voskresenskii, which was held at …

Since the late 1960s, methods of birational geometry have been used successfully in the
theory of linear algebraic groups, especially in arithmetic problems. This book--which can be …

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 …

We show that the Picard modules Pic VL (T) of projective models of algebraic tori T,
computed over a field of characteristic zero, also determine birational invariants over a field …

Using Galois theory, we explicitly construct (in all complex dimensions) an infinite family of
simple-dimensional complex tori that enjoy the following properties: the Picard number of is …

We give a stably birational classification for algebraic tori of dimensions $3 $ and $4 $ over
a field $ k $. First, we define the weak stably equivalence of algebraic tori and show that …

It is shown that the necessary condition for pure transcendence of a field of invariants given
by Swan is also sufficient. We prove the rationality of factors of the type, where the are tori of …

A complete birational classification of algebraic tori with a biquadratic splitting field is
obtained in this paper. It is shown that any torus of the indicated type is birationally …

ON TWO-DIMENSIONAL ALGEBRAIC TORI. II Page 1 Mathematics of the USSR-Izvestiya
ON TWO-DIMENSIONAL ALGEBRAIC TORI. II To cite this article: VE Voskresenskiĭ 1967 …

Examples of Algebraic Groups of Type G2 Having the Same Maximal Tori Page 1 ISSN
0081-5438, Proceedings of the Steklov Institute of Mathematics, 2016, Vol. 292, pp. 10–19. c …