De Rham intersection cohomology for general perversities

For a stratified pseudomanifold $X$, we have the de Rham Theorem $\lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t} - \per{p}}{*}{X},$ for a perversity $\per{p}$ verifying $\per{0} \leq \per{p} \leq \per{t}$, where $\per{t}$ denotes the top perversity. We extend this result to any perversity $\per{p}$. In the direction cohomology $\mapsto$ homology, we obtain the isomorphism $$\lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t} -\per{p}}{*}{X,\ib{X}{\per{p}}},$$ where ${\displaystyle \ib{X}{\per{p}} = \bigcup\_{S \preceq S\_{1} \atop \per{p} (S\_{1})< 0}S = \bigcup\_{\per{p} (S)< 0}\bar{S}.}$ In the direction homology $\mapsto$ cohomology, we obtain the isomorphism $$\lau{\IH}{\per{p}}{*}{X}=\lau{\IH}{*}{\max (\per{0},\per{t} -\per{p})}{X}.$$ In our paper stratified pseudomanifolds with one-codimensional strata are allowed.