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Essential dimension of algebraic tori
-
Roland Lötscher
,
Mark MacDonald
Published/Copyright:
March 6, 2012
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.
Received: 2010-06-13
Revised: 2011-06-24
Published Online: 2012-03-06
Published in Print: 2013-04
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Essential dimension of algebraic tori
- K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space, II: A structure theorem for r(M) > 10
- Groups of positive weighted deficiency and their applications
- The Witt group of non-degenerate braided fusion categories
- Upper motives of algebraic groups and incompressibility of Severi–Brauer varieties
- Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets
- Brauer group of moduli of principal bundles over a curve
