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
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