Nikita A. Karpenko: Incompressibility of orthogonal grassmannians

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Submission: 2011, Jun 30

We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer in the interval [1, (\dim q)/2]). If the degree of each closed point on Q is divisible by 2^i and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-incompressible.

2010 Mathematics Subject Classification: 14L17; 14C25

Keywords and Phrases: Algebraic groups, quadratic forms, projective homogeneous varieties, Chow groups and motives.

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