Saper, Leslie; Stern, Mark \(L_ 2\)-cohomology of arithmetic varieties. (English) Zbl 0653.14010 Proc. Natl. Acad. Sci. USA 84, 5516-5519 (1987). In 1982, S. Zucker [Invent. Math. 70, 169-218 (1982; Zbl 0508.20020)] conjectured that the \(L_ 2\)-cohomology groups of an arithmetic quotient of a bounded symmetric domain with respect to its natural complete Kähler metric are naturally isomorphic to the middle intersection cohomology groups of its Baily-Borel compactification. In this paper the authors give an outline of their proof of this conjecture (which has been proved recently by Looijenga for local coefficient systems of geometric origin). Reviewer: F.Kirwan Cited in 4 ReviewsCited in 4 Documents MSC: 14F99 (Co)homology theory in algebraic geometry 55N35 Other homology theories in algebraic topology 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14G99 Arithmetic problems in algebraic geometry; Diophantine geometry Keywords:\(L_ 2\)-cohomology groups; arithmetic quotient of a bounded symmetric domain; intersection cohomology; Baily-Borel compactification Citations:Zbl 0508.20020 PDFBibTeX XMLCite \textit{L. Saper} and \textit{M. Stern}, Proc. Natl. Acad. Sci. USA 84, 5516--5519 (1987; Zbl 0653.14010) Full Text: DOI