It is defined in the same way as de Rham cohomology except that one uses square-integrable differential forms.
It is closely related to intersection cohomology; indeed, the results in the preceding cited works can be expressed in terms of intersection cohomology.
Another such result is the Zucker conjecture, which states that for a Hermitian locally symmetric variety the L2 cohomology is isomorphic to the intersection cohomology (with the middle perversity) of its Baily–Borel compactification (Zucker 1982).
This was proved in different ways by Eduard Looijenga (1988) and by Leslie Saper and Mark Stern (1990).
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