Resumen de Constructible sheaves on nilpotent cones in rather good characteristic

Pramod N. Achar, Anthony Henderson, Daniel Juteau, Simon Riche

• 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.