Motivic decomposition of isotropic projective homogeneous varieties
The authors consider isotropic projective homogeneous varieties of arbitrary semisimple group over a field \(k\) and prove that the motive of such a variety is isomorphic to a direct sum of twisted motives of simpler projective homogeneous varieties. It is proved that all the information about such a decomposition is encoded in the root system of the group. To illustrate this, the authors work out the (essentially combinatorial) details for projective spaces, isotropic quadrics, and a homogeneous variety for the group of type \(E_6\). A new proof of Rost's decomposition theorem [\textit{M. Rost}, ``The motive of Pfister form'', Preprint (1998), \url{http//www.mathematik.uni-bielefeld.de/~rost/motive.html}] is given. As an application, the authors generalize Rost's nilpotence theorem to the case of arbitrary projective homogeneous varieties.
scientific article; zbMATH DE number 2147027