Essential dimension, spinor groups, and quadratic forms

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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Authors

Patrick Brosnan

University of British Columbia
Department of Mathematics
1984 Mathematics Road
Vancouver, V6T1Z2
Canada

Zinovy Reichstein

University of British Columbia
Department of Mathematics
1984 Mathematics Road
Vancouver, V6T1Z2
Canada

Angelo Vistoli

Scuola Normale Superiore
Piazza dei Cavalieri 7
56126 Pisa
Italy