Nikita A. Karpenko: Incompressibility of generic orthogonal grassmannians

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Submission: 2010, Nov 23

Given a non-degenerate quadratic form over a field such that its maximal orthogonal grassmannian is 2-incompressible (a condition satisfied for generic quadratic forms of arbitrary dimension), we apply the theory of upper motives to show that all other orthogonal grassmannians of this quadratic form are 2-incompressible. This computes the canonical 2-dimension of any projective homogeneous variety (i.e., orthogonal flag variety) associated to the quadratic form. Moreover, we show that the Chow motives with coefficients in the field of 2 elements (and therefore also in any field of characteristic 2) of those grassmannians are indecomposable. That is quite unexpected, especially after a recent result on decomposability of the motives of incompressible twisted grassmannians.

2010 Mathematics Subject Classification: 14L17; 14C25

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

Full text: dvi.gz 16 k, dvi 39 k, ps.gz 718 k, pdf.gz 107 k, pdf 128 k.

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