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Lötscher, Roland; MacDonald, Mark; Meyer, Aurel; Reichstein, Zinovy (2013): Essential dimension of algebraic tori. In: Journal für die reine und angewandte Mathematik (Crelle's Journal), No. 677: pp. 1-13


The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential dimension of a finite p-group. We obtain similar formulas for the essential p-dimension of a broad class of groups, which includes all algebraic tori.