Charles De Clercq: Motivic decompositions of projective homogeneous varieties and change of coefficients

Submission: 2010, Apr 22, revised: 2010, Sep 3

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.

2000 Mathematics Subject Classification: 20G15,16P10,14M17

Keywords and Phrases: algebraic groups, projective homogeneous varieties, motivic decompositions

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