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Incompressibility of orthogonal grassmannians

Authors
  • Karpenko, Nikita A.
Type
Preprint
Publication Date
Oct 11, 2011
Submission Date
Jul 03, 2011
Source
arXiv
License
Yellow
External links

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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