Essential dimension, spinor groups and quadratic forms
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).
Cite
@article{arxiv.0907.0922,
title = {Essential dimension, spinor groups and quadratic forms},
author = {Patrick Brosnan and Zinovy Reichstein and Angelo Vistoli},
journal= {arXiv preprint arXiv:0907.0922},
year = {2017}
}
Comments
11 pages. Accepted for publication in Annals of Mathematics