Constructible sheaves on nilpotent cones in rather good characteristic

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


We study some aspects of modular generalized Springer theory for a complex reductive group \(G\) with coefficients in a field \(\mathbb{k}\) under the assumption that the characteristic \(\ell\) of \(\mathbb{k}\) is rather good for \(G\), i.e., \(\ell\) 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-\(\ell\) generalized Springer correspondence to the characteristic-\(0\) version. We also consider Mautner's characteristic-\(\ell\) `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.

Keywords: Nilpotent cone; Springer theory.

AMS Subject Classification: Primary 17B08, 20G05.

This paper is available as a pdf (624kB) file.

Tuesday, August 4, 2015