Constructible sheaves on nilpotent cones in rather good characteristic
Tóm tắt
We study some aspects of modular generalized Springer theory for a complex reductive group G with coefficients in a field
$$\Bbbk $$
under the assumption that the characteristic
$$\ell $$
of
$$\Bbbk $$
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.
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