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We give a formula for the essential dimension of a cohomology class $\alpha$in $H^d(K, \mathbb{Q}_p/\mathbb{Z}_p (d))$ when $K$ is a strictly Henselianfield. This formula is particularly explicit in the case, where $\alpha$ is aBrauer class (for $d = 2$). As an application of our bound with $d = 3$, westudy the essential dimension of exceptional groups by examining the image ofthe Rost invariant.

Essential dimension of cohomology classes via valuation theory