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Chow motives of twisted flag varieties

B. Calmes·V. Petrov·N. Semenov·K. Zainoulline
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Abstract

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.

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B. Calmes, V. Petrov, N. Semenov, K. Zainoulline. 2005-07-08. Chow motives of twisted flag varieties. https://arxiv.org/abs/math/0505242

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