Essential dimension of algebraic tori

Lötscher, Roland and MacDonald, Mark and Meyer, Aurel and Reichstein, Zinovy (2013) Essential dimension of algebraic tori. Journal für die reine und angewandte Mathematik (Crelle's Journal), 677. pp. 1-13. ISSN 0075-4102

Abstract

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.