brosnan@math.ubc.ca, reichst@math.ubc.ca and angelo.vistoli@sns.it

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

Full text: dvi.gz 24 k, dvi 50 k, ps.gz 703 k, pdf.gz 140 k, pdf 160 k.

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