Tel Aviv University
R-equivalence on linear algebraic groups
Friday 8th August, 12:05-12:55pm,
Let X be a smooth algebraic variety over a field k.
Manin in 1972 introduced the notion of R-equivalence on
(the definition will be given in the talk). Let X(k)/R
denote the set of classes of R-equivalence. Colliot-Thelene
and Sansuc in 1977 computed the group T(k)/R, where
T is a k-torus.
Assume that k is a p-adic field, or a totally imaginary
number field, or k=k_0(S), where
k_0 is an algebraically closed
field of characteristic 0 and S is a k_0-surface.
It is known that for such
a field k we have G(k)/R=1 for any
simply connected semisimple group G.
Using this fact, we compute G(k)/R
for any connected linear k-group G,
and prove that the abelian group G(k)/R is a
k-birational invariant of G.
This is a joint work with B. Kunyavskii and P. Gille.