Zero Cycles on a Twisted Cayley Plane

http://dx.doi.org/10.4153/CMB-2008-013-2
Canad. Math. Bull. 51(2008), 114-124

  Published:2008-03-01
 Printed: Mar 2008

Let $k$ be a field of characteristic not $2,3$. Let $G$ be an exceptional simple algebraic group over $k$ of type $\F$, $^1{\E_6}$ or $\E_7$ with trivial Tits algebras. Let $X$ be a projective $G$-homogeneous variety. If $G$ is of type $\E_7$, we assume in addition that the respective parabolic subgroup is of type $P_7$. The main result of the paper says that the degree map on the group of zero cycles of $X$ is injective.