For having a Poincaré duality between the intersection homology of a pseudomanifold and the cohomology given by the dual complex, one needs a coefficient field or an extra-hypothesis on the torsion. In this talk, by using the classical process of blowing-up adapted to a simplicial setting, we build a cochain complex which gives a Poincaré duality with intersection homology of a paracompact pseudomanifold, for any commutative ring of coefficients. We show that this cohomology coincides with the Goresky-MacPherson cohomology for any compact separable CS-set in the case of a coefficient field, the result remaining true also for a paracompact separable pseudomanifold, locally free and a Dedekind ring.

Coauthors: David Chataur (Unniversité d'Amiens, France) Daniel Tanré (Université de Lille 1, France)