Essential dimension of simple algebras with involutions

Abstract

Let 1 < m < n be integers with m vertical bar n and Alg(n, m) the class of central simple algebras of degree n and exponent dividing m. In this paper, we find new, improved upper bounds for the essential dimension and two-dimension of Alg(n, 2). In particular, we show that ed(2)(Alg(16, 2))=24 over a field F of characteristic different from 2.