On Euler characteristic of equivariant sheaves

Alexander Braverman

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1 Citation (Scopus)


Let k be an algebraically closed field of characteristic p > 0 and let ℓ be another prime number. Gabber and Looser proved that for any algebraic torus T over k and any perverse ℓ-adic sheaf F on T the Euler characteristic χ(F) is non-negative. We conjecture that the same result holds for any perverse sheaf F on a reductive group G over k which is equivariant with respect to the adjoint action. We prove the conjecture when F 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.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalAdvances in Mathematics
Issue number1
Publication statusPublished - 15 Oct 2003
Externally publishedYes


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