  In his paper, 'On torsion in the cohomology of locally symmetric varieties',
Peter Scholze has introduced a new, purely topological method to construct the
cohomology classes on arithmetic quotients of symmetric spaces of rational
reductive groups originating from the cohomology of the similar quotients of
Levi subgroups of maximal parabolic subgroups. We extend this construction
beyond the cases he considers, and, in the complex case, to the cohomology of
local systems.
