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Essential dimension of algebraic tori

Research output: Contribution to journalJournal article

Published

<mark>Journal publication date</mark>04/2013
<mark>Journal</mark>Journal für die reine und angewandte Mathematik (Crelle's Journal)
Volume677
Number of pages13
Pages1-13
Early online date29/03/13
<mark>Original language</mark>English

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.