Patrick Brosnan, Zinovy Reichstein, and Angelo Vistoli: Essential dimension, spinor groups and quadratic forms, and

Submission: 2009, Jul 5

We prove that the essential dimension of the spinor group Spin_n grows exponentially with n; in particular, we give a precise formula for this essential dimension when n is not divisible by 4. We use this result to show that the number of 3-fold Pfister forms needed to represent the Witt class of a general quadratic form of rank n with trivial discriminant and Hasse-Witt invariant grows exponentially with n. This paper represents a reworking and refinement of some of the results from our earlier preprints 238 and 275.

2000 Mathematics Subject Classification: 11E04, 11E72, 15A66

Keywords and Phrases: Essential dimension, spinor group, quadratic form, Witt group, Pfister form

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