Motivic decompositions of projective homogeneous varieties and change of coefficients

Details Motivic decompositions of projective homogeneous varieties and change of coefficients Motivic decompositions of projective homogeneous varieties and change of coefficients

2010-04-26

arxiv.org/abs/1004.4417v2

Mathematics

Algebraic Geometry

Scientific paper

We prove that under some assumptions on an algebraic group $G$, indecomposable direct summands of the motive of a projective $G$-homogeneous variety with coefficients in $\mathbb{F}_p$ remain indecomposable if the ring of coefficients is any field of characteristic $p$. In particular for any projective $G$-homogeneous variety $X$, the decomposition of the motive of $X$ in a direct sum of indecomposable motives with coefficients in any finite field of characteristic $p$ corresponds to the decomposition of the motive of $X$ with coefficients in $\mathbb{F}_p$. We also construct a counterexample to this result in the case where $G$ is arbitrary.

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