arXiv: Experimental full text search
Some publication(s) by Harris related to Shimura varieties.
AAG (Arithmetic algebraic geometry)
Arithmetic, Later
Harris and Zucker, also subsequent papers
A Google search on boundary cohomology gives various things on boundary cohomology of Shimura varieties. This seems to be the only context where the term boundary cohomology is used.
nLab page on Boundary cohomology