Upper Motives of Outer Algebraic Groups

  title={Upper Motives of Outer Algebraic Groups},
  author={Nikita A. Karpenko},
Let G be a semisimple affine algebraic group over a field F . Let E/F be a minimal field extension such that the group GE 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… CONTINUE READING
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