# intersection cohomology and etale cohomology

Hello,

Can someone explain or give a reference on the comparison between intersection cohomology and l-adic etale cohomology of a variety over a field of characteristic zero?

Thanks!

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The only general link I know is the fact that intersection cohomology with coefficients in ${\bf Q}_l$ is isomorphic to étale cohomology if the variety is non-singular. Otherwise, there is no link: the first is the cohomology of the intersection complex IC, which only coincides with the constant system ${\bf Q}_l$ if the variety is non-singular. See any introduction to perverse sheaves, for instance the introduction by Migliorini and de Cataldo (see ams.org/journals/bull/2009-46-04/S0273-0979-09-01260-9/…) or the original article "BBD" (see ref. in intro.) – Damian Rössler Feb 6 '13 at 13:56
Intersection cohomology (in the context of the etale topology) generalizes the usual l-adic cohomology. With the appropriate choice of the perversity, intersection cohomology gives the usual l-adic cohomology, with or without compact support. – anon Feb 6 '13 at 18:30
@anon: I was implicitly referring to middle perversity. – Damian Rössler Feb 8 '13 at 15:48