Abstract
We prove that the essential dimension of the spinor group $\mathbf{Spin}_n$ grows exponentially with $n$ and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more complex, in high dimensions, than previously expected.
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@book {adams, MRKEY = {1428422},
AUTHOR = {Adams, J. F.},
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TITLE={Essential dimension},
BOOKTITLE={Quadratic Forms --- Algebra, Arithmetic , and Geometry},
NOTE={(R. Baeza, W. K. Chan, D. W. Hoffman, and R. Schulze-Pillot, eds.)},
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author={Meyer, A. and Reichstein, Z.},
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NOTE={{\it Documenta Math.},
to appear},
ARXIV={0811.2517},
} -
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author={Parimala, R. and Suresh, V. and Tignol, J.-P.},
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BOOKTITLE={Quadratic Forms --- Algebra, Arithmetic, and Geometry},
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}