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On Euler Characteristic of equivariant sheaves
Let be an algebraically closed field of characteristic and let
be another prime number. O. Gabber and F. Loeser proved that for any
algebraic torus over and any perverse -adic sheaf \calF on
the Euler characteristic \chi(\calF) is non-negative.
We conjecture that the same result holds for any perverse sheaf \calF on a
reductive group over which is equivariant with respect to the adjoint
action. We prove the conjecture when \calF is obtained by Goresky-MacPherson
extension from the set of regular semi-simple elements in . From this we
deduce that the conjecture holds for of semi-simple rank 1
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