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arXiv · 1107.0438

Incompressibility of orthogonal grassmannians

Nikita A. Karpenko
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Abstract

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.

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Nikita A. Karpenko. 2011-07-03. Incompressibility of orthogonal grassmannians. https://arxiv.org/abs/1107.0438

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