 Intersection cohomology

In the Deligne-sheaf convention, $I{H}_{\bar{p}}^i(X)={\mathbb{H}}^i(X,I{C}_{\bar{p}})$, with $I{C}_{\bar{p}}$ normalized in degree zero on the regular stratum. For a compact oriented $N$-dimensional pseudomanifold over a field, $I{H}_{\bar{p}}^i(X)\cong I{H}_{N-i}^{\bar{p}}(X)$ and it is dual to $I{H}_i^{\bar{q}}(X)$, where $\bar{p}(k)+\bar{q}(k)=k-2$. Thus the dual of lower-middle singular chains uses the upper-middle Deligne sheaf. The two middle conventions agree on Witt spaces.