Motivic decompositions of projective homogeneous varieties and change of coefficients

2010/04/26 by Charles De Clercq, De Clercq, Charles
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1004.4417

arxiv created 2010/09/03 · arxiv updated 2010/09/06

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 \mathbbF_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 \mathbbF_p. We also construct a counterexample to this result in the case where G is arbitrary.

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