A lower bound on the essential dimension of a connected linear group

• Autores: Philippe Gille, Zinovy Reichstein
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 84, Nº 1, 2009, págs. 189-212
• Idioma: inglés
• DOI: 10.4171/cmh/158
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• Resumen

  • Let G be a connected linear algebraic group defined over an algebraically closed field k and H be a finite abelian subgroup of G whose order does not divide char(k). We show that the essential dimension of G is bounded from below by rank(H) - rank?CG(H)0, where rank?CG(H)0 denotes the rank of the maximal torus in the centralizer CG(H). This inequality, conjectured by J.-P. Serre, generalizes previous results of Reichstein�Youssin (where char(k) is assumed to be 0 and CG(H) to be finite) and Chernousov�Serre (where H is assumed to be a 2-group).