Constructible sheaves on nilpotent cones in rather good characteristic

• Pramod N. Achar ^[1] ; Anthony Henderson ^[2] ; Daniel Juteau ^[4] ; Simon Riche ^[3]
  1. [1] Louisiana State University

     Louisiana State University

     Estados Unidos

     
  2. [2] University of Sydney

     University of Sydney

     Australia

     
  3. [3] Blaise Pascal University

     Blaise Pascal University

     Arrondissement de Clermont-Ferrand, Francia

     
  4. [4] Université de Caen

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 203-243
• Idioma: inglés
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• Resumen

  • We study some aspects of modular generalized Springer theory for a complex reductive group G with coefficients in a field k under the assumption that the characteristic of k is rather good for G, i.e. is good and does not divide the order of the component group of the centre of G. We prove a comparison theorem relating the characteristic- generalized Springer correspondence to the characteristic-0 version.

    We also consider Mautner’s characteristic- ‘cleanness conjecture’; we prove it in some cases; and we deduce several consequences, including a classification of supercuspidal sheaves and an orthogonal decomposition of the equivariant derived category of the nilpotent cone.

    P.