Abstract
Let 1⩽m⩽n be integers with m|n and Algn, 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 Algn, 2. In particular, we show that ed2(Alg16, 2)=24 over a field F of characteristic different from 2.
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