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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.

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Selecta Mathematica, New Series

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