Nikita Karpenko and Alexander Merkurjev: Rost projectors and Steenrod operations

Submission: 2002, Jun 22

Let X be an anisotropic projective quadric possessing a Rost Rost projector rho. We compute the 0-dimensional component of the total Steenrod operation on the modulo 2 Chow group of the Chow motive given by the projector rho. The result allows to compute the whole integral Chow group of every excellent quadric. On the other hand, the result is being applied to show that the integer dimX+1 is a power of 2.

2000 Mathematics Subject Classification: 11E04; 14C25

Keywords and Phrases: Quadratic forms, first Witt index, Chow groups, Steenrod operations, correspondences.

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