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arXiv · 0907.0922

Essential dimension, spinor groups and quadratic forms

Patrick Brosnan·Zinovy Reichstein·Angelo Vistoli
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Abstract

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 overlaps with our earlier preprint arXiv:math/0701903 . That preprint has splintered into several parts, which have since acquired a life of their own. In particular, see "Essential dimension of moduli of curves and other algebraic stacks", by the same authors, and "Some consequences of the Karpenko-Merkurjev theorem", by Meyer and Reichstein (arXiv:0811.2517).

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Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli. 2009-07-06. Essential dimension, spinor groups and quadratic forms. https://arxiv.org/abs/0907.0922

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