karpenko at math.jussieu.fr

Submission: 2009, Jun 16

Let G be a semisimple affine algebraic group over a field F. Let E/F be a minimal field extension such that the group G_E is of inner type. Assuming that the degree of E/F is a power of a prime p, we determine the structure of the Chow motives with coefficients in a finite field of characteristic p of the projective G-homogeneous varieties. More precisely, it is known that the motive of any such variety decomposes (in a unique way) into a sum of indecomposable motives, and we describe the indecomposable summands which appear in the decompositions. This description is already known for the groups G of inner type and is new for G of outer type.

2000 Mathematics Subject Classification: 14L17; 14C25

Keywords and Phrases: Algebraic groups, projective homogeneous varieties, Chow groups

Full text: dvi.gz 17 k, dvi 39 k, ps.gz 680 k, pdf.gz 114 k, pdf 137 k.

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