Chow motives of twisted flag varieties, by Baptiste Calmes, Viktor Petrov, Nikita Semenov, and Kirill Zainoulline

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB_2(A), where A is a division algebra of degree 5, into a direct sum of two indecomposable motives. As an application we provide another counter-example to the uniqueness of a direct sum decomposition in the category of motives with integral coefficients.


Baptiste Calmes <bcalmes@math.uni-bielefeld.de>
Viktor Petrov <victor@vp11701.spb.edu>
Nikita Semenov <>
Kirill Zainoulline <kirill@math.uni-bielefeld.de>