Preprint

Constructible sheaves on nilpotent cones in rather good characteristic

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


Abstract

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.

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Tuesday, August 4, 2015