Scholars@Duke
Leslie Saper

Leslie Saper

Professor of Mathematics
Mathematics
saper@duke.edu
Box 90320, Dept. of Mathematics, Durham, NC 27708-0320
120 Science Dr, Room 110 Physics Building, Durham, NC 27708-0320
Office hours

Selected Publications

Remembering Steve Zucker

Journal Article Notices of the American Mathematical Society · August 2, 2021 Featured Publication Open Access Cite

Perverse sheaves and the reductive Borel-Serre compactification

Chapter · 2017 Featured Publication We briefly introduce the theory of perverse sheaves with special attention to the topological situation where strata can have odd dimension. This is part of a project to use perverse sheaves on the topological reductive Borel-Serre compactification of a He ... Link to item Cite

The fundamental group of reductive Borel–Serre and Satake compactifications

Journal Article Asian Journal of Mathematics · 2015 Let G be an almost simple, simply connected algebraic group defined over a number field k, and let S be a finite set of places of k including all infinite places. Let X be the product over v ε S of the symmetric spaces associated to G(kv), when v is an inf ... Full text Cite

L²-cohomology of locally symmetric spaces. I

Journal Article Pure and Applied Mathematics Quarterly · 2005 Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in [math.RT/0112251]. Th ... Full text Link to item Cite

ℒ-modules and the conjecture of Rapoport and Goresky-Macpherson

Chapter · 2005 Featured Publication Consider the middle perversity intersection cohomology groups of various compactifications of a Hermitian locally symmetric space. Rapoport and independently Goresky and MacPherson have conjectured that these groups coincide for the reductive Borel-Serre c ... Link to item Cite

Geometric rationality of equal-rank Satake compactifications

Journal Article Mathematical Research Letters · 2004 Satake has constructed compactifications of symmetric spaces D=G/K which (under a condition called geometric rationality by Casselman) yield compactifications of the corresponding locally symmetric spaces. The different compactifications depend on the choi ... Link to item Cite

On the Cohomology of Locally Symmetric Spaces and of their Compactifications

Chapter · 2003 This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the intersection cohom ... Link to item Cite

Tilings and finite energy retractions of locally symmetric spaces

Journal Article Commentarii Mathematici Helvetici · January 1, 1997 Let Γ\X̄ be the Borel-Serre compactification of an arithmetic quotient Γ\X of a symmetric space of noncompact type. We construct natural tilings Γ\X̄ = ∐P Γ\X̄P (depending on a parameter b) which generalize the Arthur-Langlands partition ... Full text Cite

L²-cohomology of Kähler varieties with isolated singularities

Journal Article Journal of Differential Geometry · 1992 Link to item Cite

Intersection cohomology of cs-spaces and Zeeman's filtration

Journal Article Inventiones Mathematicae · 1991 Full text Cite

L²-cohomology of arithmetic varieties

Journal Article Annals of Mathematics · 1990 Link to item Cite

L²-cohomology of arithmetic varieties

Journal Article Proc Natl Acad Sci U.S.A. · August 1987 The L₂-cohomology of arithmetic quotients of bounded symmetric domains is studied. We establish the conjecture of Zucker equating the L₂-cohomology of these spaces to the intersection cohomology of their Baily-Borel compactifications. ... Link to item Cite

ℒ-modules and micro-support

Journal Article to appear in Annals of Mathematics Featured Publication Link to item Cite