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Motivic decompositions of projective homogeneous varieties and change of coefficients

Research paper by Charles De Clercq

Indexed on: 03 Sep '10Published on: 03 Sep '10Published in: Mathematics - Algebraic Geometry



Abstract

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.