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# Zero Cycles on a Twisted Cayley Plane

Published:2008-03-01
Printed: Mar 2008
• V. Petrov
• N. Semenov
• K. Zainoulline
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## Abstract

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.
 MSC Classifications: 20G15 - Linear algebraic groups over arbitrary fields 14C15 - (Equivariant) Chow groups and rings; motives

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