Z. Reichstein, Higher trace forms and essential dimension in central simple algebras, Archiv der Mathematik, 88, no. 1 (2007), 12--18. Posted March 2006.

Abstract: Let A/K be a finite-dimensional central simple algebra and Tr be the reduced trace function in A. We show that the essential dimension of A is captured by the r-linear trace form (a_1, ..., a_r) -> Tr(a_1 ... a_r), for any r >= 3.

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