On the reductive Borel-Serre compactification: L p-cohomology of arithmetic groups (for large p)

Here, the left-hand side is the L-cohomology of M with respect to a (locally) invariant metric. Though it would be more natural to allow p = ∞ in Theorem 1, this is not generally possible (see (3.2.2)). On the other hand, there is a natural mapping H (∞)(M) → H • (p)(M) when p < ∞, because M has finite volume. The definition of M is recalled in (1.9). Theorem 1 can be viewed as an analogue of the so-called Zucker conjecture (in the case of constant coefficients), where p = 2: