= Intersection-complex support and cosupport axioms
For an isolated singular point of an $N$-dimensional oriented pseudomanifold, the unshifted middle <intersection complex> restricts to $\mathbb Q$ on the regular stratum and has no negative <cohomology>. Its support condition is $H^j(i_x^*IC_{\bar p})=0$ for $j>\bar p(N)$; its cosupport condition is $H^j(i_x^!IC_{\bar p})=0$ for $j\le\bar p(N)+1$. These conditions, together with constructibility and normalization, characterize it. On a <Witt space> they are exchanged by $IC\cong D(IC)[-N]$.
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