Essential p-dimension of algebraic tori

2009/10/29 by Roland Lötscher, Mark L. MacDonald, Lötscher, Roland +6 · 1 citation
Mathematics · #20G15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20G15

paper · pdf · doi:10.48550/arxiv.0910.5574

30 pages, no figures

arxiv created 2009/10/29 · openalex publication_date 2009/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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 broader class of groups, which includes all algebraic tori.

Cited by

• Essential p-dimension of algebraic groups whose connected component is a torus

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