Constructible sheaves on nilpotent cones in rather good characteristic

Pramod N. Achar (1) , Anthony Henderson (2) , Daniel Juteau (3) , Simon Riche (4, 5)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 School of Mathematics and statistics [Sydney]
3 LMNO - Laboratoire de Mathématiques Nicolas Oresme
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
5 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 l of k is rather good for G, i.e., l 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-l generalized Springer correspondence to the characteristic-0 version. We also consider Mautner's characteristic-l '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.

Domaines: Mathématiques [math]

Pramod N. Achar, Anthony Henderson, Daniel Juteau, Simon Riche. Constructible sheaves on nilpotent cones in rather good characteristic. Selecta Mathematica (New Series), 2017, 23, pp.203-243. ⟨hal-01223124⟩