Submission: 2009, Oct 28
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 broader class of groups, which includes all algebraic tori.
2000 Mathematics Subject Classification: 20G15
Keywords and Phrases: Essential dimension, algebraic torus, twisted finite group, lattice
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