2002/02/18 by Alexander Braverman, Braverman, Alexander
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.math/0202165
arxiv created 2002/02/18 · arxiv updated 2009/11/30
Let k be an algebraically closed field of characteristic p>0 and let ℓ be another prime number. O. Gabber and F. Loeser proved that for any algebraic torus T over k and any perverse ℓ-adic sheaf \calF on T the Euler characteristic χ(\calF) is non-negative. We conjecture that the same result holds for any perverse sheaf \calF on a reductive group G over k 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 G. From this we deduce that the conjecture holds for G of semi-simple rank 1.