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Publications of Leslie Saper    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds320773,
   Author = {Saper, L},
   Title = {ℒ-modules and micro-support},
   Journal = {To Appear in Annals of Mathematics},
   Year = {2018},
   Key = {fds320773}
}

@article{fds320662,
   Author = {Saper, L},
   Title = {Perverse sheaves and the reductive Borel-Serre
             compactification},
   Volume = {39},
   Pages = {555-581},
   Booktitle = {Hodge Theory and L²-analysis},
   Publisher = {International Press},
   Editor = {Ji, L},
   Year = {2017},
   Abstract = {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 Hermitian locally symmetric space as a
             tool to study perverse sheaves on the Baily-Borel
             compactification, a projective algebraic variety. We sketch
             why the decomposition theorem holds for the natural map
             between the reductive Borel-Serre and the Baily-Borel
             compactifications. We demonstrate how to calculate
             extensions of simple perverse sheaves on the reductive
             Borel-Serre compactification and illustrate with the example
             of Sp(4,R).},
   Key = {fds320662}
}

@article{fds320536,
   Author = {Ji, L and Murty, VK and Saper, L and Scherk, J},
   Title = {The fundamental group of reductive Borel–Serre and Satake
             compactifications},
   Journal = {Asian Journal of Mathematics},
   Volume = {19},
   Number = {3},
   Pages = {465-486},
   Publisher = {International Press of Boston},
   Year = {2015},
   url = {http://www.intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0019/0003/a004/},
   Abstract = {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 infinite place, and the Bruhat-Tits
             buildings associated to G(kv), when v is a finite place. The
             main result of this paper is to compute explicitly the
             fundamental group of the reductive Borel-Serre
             compactification of Γ\X, where Γ is an S-arithmetic
             subgroup of G. In the case that G is neat, we show that this
             fundamental group is isomorphic to Γ/EΓ, where EΓ is the
             subgroup generated by the elements of Γ belonging to
             unipotent radicals of k-parabolic subgroups. Analogous
             computations of the fundamental group of the Satake
             compactifications are made. It is noteworthy that
             calculations of the congruence subgroup kernel C(S, G) yield
             similar results.},
   Doi = {10.4310/AJM.2015.v19.n3.a4},
   Key = {fds320536}
}

@article{fds37687,
   Author = {Leslie D. Saper},
   Title = {$\mathscr L$-modules and the conjecture of Rapoport
             and Goresky-MacPherson},
   Volume = {298},
   Series = {Astérisque},
   Pages = {319--334},
   Booktitle = {Formes Automorphes (I) -- Actes du Semestre du Centre
             Émile Borel, printemps 2000},
   Publisher = {Société Mathématique de
             France},
   Editor = {J. Tilouine and H. Carayol and M. Harris and M.-F.
             Vignéras},
   Year = {2005},
   MRNUMBER = {2141706},
   url = {http://arxiv.org/abs/math/0112250},
   Keywords = {Intersection cohomology • Shimura varieties •
             locally symmetric spaces • compactifications},
   Abstract = {<a href="http://smf.emath.fr/Publications/Asterisque/2005/298/html/smf_ast_298_319-334.html">click
             here for abstract of published paper</a>},
   Key = {fds37687}
}

@article{fds244104,
   Author = {Saper, L},
   Title = {ℒ-modules and the conjecture of Rapoport and
             Goresky-Macpherson},
   Volume = {298},
   Number = {298},
   Pages = {319-334},
   Booktitle = {Formes Automorphes (I) — Actes du Semestre du Centre
             Émile Borel, printemps 2000},
   Editor = {Tilouine, J and Carayol, H and Harris, M and Vignéras,
             M-F},
   Year = {2005},
   ISBN = {2-85629-172-4},
   ISSN = {0303-1179},
   Abstract = {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 compactification and the
             Baily-Borel-Satake compactification. This paper describes
             the theory of ℒ-modulcs and how it is used to solve the
             conjecture. More generally we consider a Satake
             compactification for which all real boundary components are
             equal-rank. Details will be given elsewhere, As another
             application of ℒ-modules, we prove a vanishing theorem for
             the ordinary cohomology of a locally symmetric space. This
             answers a question raised by Tilouine.},
   Key = {fds244104}
}

@article{fds305514,
   Author = {Saper, L},
   Title = {L²-cohomology of locally symmetric spaces.
             I},
   Journal = {Pure and Applied Mathematics Quarterly},
   Volume = {1},
   Number = {4},
   Pages = {889-937},
   Publisher = {International Press of Boston},
   Year = {2005},
   MRNUMBER = {2201005},
   url = {http://arxiv.org/abs/math/0412353v3},
   Abstract = {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]. That paper also introduced
             the micro-support of an L-module, a combinatorial invariant
             that to a great extent characterizes the cohomology of the
             associated sheaf. The theory has been successfully applied
             to solve a number of problems concerning the intersection
             cohomology and weighted cohomology of the reductive
             Borel-Serre compactification [math.RT/0112251], as well as
             the ordinary cohomology of X [math.RT/0112250]. In this
             paper we extend the theory so that it covers L²-cohomology.
             In particular we construct an L-module whose cohomology is
             the L²-cohomology of X and we calculate its micro-support.
             As an application we obtain a new proof of the conjectures
             of Borel and Zucker.},
   Doi = {10.4310/PAMQ.2005.v1.n4.a9},
   Key = {fds305514}
}

@article{fds244105,
   Author = {Saper, L},
   Title = {Geometric rationality of equal-rank Satake
             compactifications},
   Journal = {Mathematical Research Letters},
   Volume = {11},
   Number = {5},
   Pages = {653-671},
   Publisher = {International Press of Boston},
   Year = {2004},
   MRNUMBER = {2106233},
   url = {http://arxiv.org/abs/math/0211138v4},
   Abstract = {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 choice of a representation of G. One example
             is the Baily-Borel-Satake compactification of a Hermitian
             locally symmetric space; Baily and Borel proved this is
             always geometrically rational. Satake compactifications for
             which all the real boundary components are equal-rank
             symmetric spaces are a natural generalization of the
             Baily-Borel-Satake compactification. Recent work (see
             math.RT/0112250, math.RT/0112251) indicates that this is the
             natural setting for many results about cohomology of
             compactifications of locally symmetric spaces. In this paper
             we prove any Satake compactification for which all the real
             boundary components are equal-rank symmetric spaces is
             geometrically rational aside from certain rational rank 1 or
             2 exceptions; we completely analyze geometric rationality
             for these exceptional cases. The proof uses Casselman's
             criterion for geometric rationality. We also prove that a
             Satake compactification is geometrically rational if the
             representation is defined over the rational
             numbers.},
   Doi = {10.4310/mrl.2004.v11.n5.a9},
   Key = {fds244105}
}

@article{fds320537,
   Author = {Saper, L},
   Title = {On the Cohomology of Locally Symmetric Spaces and of their
             Compactifications},
   Pages = {219-289},
   Booktitle = {Current developments in mathematics, 2002},
   Publisher = {International Press},
   Editor = {Jerison, D and Lusztig, G and Mazur, B and Mrowka, T and Schmid, W and Stanley, R and Yau, S-T},
   Year = {2003},
   MRNUMBER = {2062320},
   url = {http://arxiv.org/abs/math/0306403},
   Abstract = {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 cohomology of a real equal-rank
             Satake compactification of a locally symmetric space with
             that of the reductive Borel-Serre compactification. We
             motivate the conjecture with examples and then give an
             introduction to the various topics that are involved:
             intersection cohomology, the derived category, and
             compactifications of a locally symmetric space, particularly
             those above. We then give an overview of the theory of
             L-modules and micro-support (see math.RT/0112251) which was
             developed to solve the conjecture but has other important
             applications as well. We end with sketches of the proofs of
             three main theorems on L-modules that lead to the resolution
             of the conjecture. The text is enriched with many examples,
             illustrations, and references to the literature.},
   Key = {fds320537}
}

@article{fds244108,
   Author = {Saper, L},
   Title = {Tilings and finite energy retractions of locally symmetric
             spaces},
   Journal = {Commentarii Mathematici Helvetici},
   Volume = {72},
   Number = {2},
   Pages = {167-201},
   Publisher = {Research Institute for Mathematical Sciences, Kyoto
             University},
   Year = {1997},
   Month = {December},
   MRNUMBER = {99a:22019},
   url = {http://dx.doi.org/10.1007/pl00000369},
   Abstract = {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 of Γ\X. This is applied to yield
             a natural piecewise analytic deformation retraction of
             Γ\X̄ onto a compact submanifold with corners Γ\X0 ⊂
             Γ\X. In fact, we prove that Γ\X0 is a realization (under a
             natural piecewise analytic diffeomorphism) of Γ\X̄ inside
             the interior Γ\X. For application to the theory of harmonic
             maps and geometric rigidity, we prove this retraction and
             diffeomorphism have finite energy except for a few low rank
             examples. We also use tilings to give an explicit
             description of a cofinal family of neighborhoods of a face
             of Γ\X̄, and study the dependance of tilings on the
             parameter b and the degeneration of tilings.},
   Doi = {10.1007/pl00000369},
   Key = {fds244108}
}

@article{fds320484,
   Author = {Saper, L},
   Title = {L²-cohomology of the Weil-Peterson metric},
   Volume = {150},
   Pages = {345-360},
   Booktitle = {Mapping Class Groups and Moduli Spaces of Riemann Surfaces
             Proceedings of Workshops Held June 24-28, 1991, in
             Göttingen, Germany, and August 6-10, 1991, in Seattle,
             Washington},
   Publisher = {Amer. Math. Soc.},
   Editor = {Bödigheimer, C-F and Hain, R},
   Year = {1993},
   ISBN = {0821851675},
   MRNUMBER = {94j:32014},
   url = {http://www.ams.org/mathscinet-getitem?mr=94j:32014},
   Key = {fds320484}
}

@article{fds9231,
   Author = {Leslie D. Saper and Mark Stern},
   Title = {Appendix to: On the shape of the contribution of a fixed
             point on the boundary. The case of Q-rank one, by M.
             Rapoport},
   Booktitle = {The Zeta Functions of Picard Modular Surfaces},
   Publisher = {Les Publications CRM, Montréal},
   Editor = {R. Langlands and D. Ramakrishnan},
   Year = {1992},
   MRNUMBER = {93e:11070b},
   url = {http://www.ams.org/mathscinet-getitem?mr=93e:11070b},
   Key = {fds9231}
}

@article{fds244107,
   Author = {Saper, L},
   Title = {L²-cohomology of Kähler varieties with isolated
             singularities},
   Journal = {Journal of Differential Geometry},
   Volume = {36},
   Number = {1},
   Pages = {89-161},
   Publisher = {International Press of Boston},
   Year = {1992},
   ISSN = {1945-743X},
   MRNUMBER = {93e:32038},
   url = {http://dx.doi.org/10.4310/jdg/1214448444},
   Doi = {10.4310/jdg/1214448444},
   Key = {fds244107}
}

@article{fds320485,
   Author = {Saper, L and Stern, M},
   Title = {Appendix to: On the shape of the contribution of a fixed
             point on the boundary. The case of Q-rank one, by M.
             Rapoport},
   Pages = {489-491},
   Booktitle = {The zeta functions of Picard modular surfaces based on
             lectures delivered at a CRM Workshop in the spring of
             1988},
   Publisher = {Centre De Recherches Mathématiques},
   Editor = {Langlands, R and Ramakrishnan, D},
   Year = {1992},
   Key = {fds320485}
}

@article{fds244103,
   Author = {Habegger, N and Saper, L},
   Title = {Intersection cohomology of cs-spaces and Zeeman's
             filtration},
   Journal = {Inventiones Mathematicae},
   Volume = {105},
   Number = {1},
   Pages = {247-272},
   Publisher = {Springer Nature},
   Year = {1991},
   Month = {December},
   ISSN = {0020-9910},
   MRNUMBER = {92k:55010},
   url = {http://dx.doi.org/10.1007/BF01232267},
   Doi = {10.1007/BF01232267},
   Key = {fds244103}
}

@article{fds320486,
   Author = {Saper, L},
   Title = {L₂-cohomology of algebraic varieties},
   Volume = {1},
   Pages = {735-746},
   Booktitle = {Proceedings of the International Congress of Mathematicians,
             August 21-29, 1990, Kyoto},
   Publisher = {Springer-Verlag},
   Editor = {Satake, I},
   Year = {1991},
   ISBN = {0387700471},
   MRNUMBER = {93e:32037},
   url = {http://www.ams.org/mathscinet-getitem?mr=93e:32037},
   Key = {fds320486}
}

@article{fds320487,
   Author = {Saper, L and Zucker, S},
   Title = {An introduction to L²-cohomology},
   Volume = {52, Part 2},
   Pages = {519-534},
   Booktitle = {Several Complex Variables and Complex Geometry},
   Publisher = {Amer. Math. Soc.},
   Year = {1991},
   ISBN = {0821814907},
   MRNUMBER = {92k:14023},
   url = {http://www.ams.org/mathscinet-getitem?mr=92k:14023},
   Key = {fds320487}
}

@article{fds320488,
   Author = {SAPER, L and STERN, M},
   Title = {L2-COHOMOLOGY OF ARITHMETIC VARIETIES},
   Journal = {Annals of Mathematics},
   Volume = {132},
   Number = {1},
   Pages = {1-69},
   Publisher = {JSTOR},
   Year = {1990},
   Month = {July},
   MRNUMBER = {91m:14027},
   url = {http://dx.doi.org/10.2307/1971500},
   Doi = {10.2307/1971500},
   Key = {fds320488}
}

@article{fds320489,
   Author = {Saper, L and Stern, M},
   Title = {L²-cohomology of arithmetic varieties},
   Journal = {Proceedings of the National Academy of Sciences of the
             United States of America},
   Volume = {84},
   Number = {16},
   Pages = {5516-5519},
   Year = {1987},
   Month = {August},
   MRNUMBER = {89g:32052},
   url = {http://dx.doi.org/10.1073/pnas.84.16.5516},
   Abstract = {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.},
   Doi = {10.1073/pnas.84.16.5516},
   Key = {fds320489}
}

@article{fds244102,
   Author = {Saper, L},
   Title = {L₂-cohomology and intersection homology of certain
             algebraic varieties with isolated singularities},
   Journal = {Inventiones Mathematicae},
   Volume = {82},
   Number = {2},
   Pages = {207-255},
   Publisher = {Springer Nature},
   Year = {1985},
   ISSN = {0020-9910},
   MRNUMBER = {87h:32029},
   url = {http://dx.doi.org/10.1007/BF01388801},
   Doi = {10.1007/BF01388801},
   Key = {fds244102}
}


%% Preprints   
@article{fds213234,
   Author = {L. Ji and K. Murty and L. Saper and J. Scherk},
   Title = {The Congruence Subgroup Kernel and the Fundamental Group of
             the Reductive Borel-Serre Compactification},
   Year = {2011},
   Month = {June},
   url = {http://arxiv.org/abs/1106.4810},
   Abstract = {Let <b>G</b> be an almost simple, simply connected algebraic
             group defined over a number field <i>k</i>, and let <i>S</i>
             be a finite set of places of <i>k</i> including all infinite
             places. Let <i>X</i> be the product over
             <nobr><i>v</i>&thinsp;&isin;&thinsp;<i>S</i></nobr> of the
             symmetric spaces associated to <b>G</b>(<i>k<sub>v</sub></i>),
             when <i>v</i> is an infinite place, and the Bruhat-Tits
             buildings associated to <b>G</b>(<i>k<sub>v</sub></i>), when
             <i>v</i> is a finite place. The main result of this paper is
             to identify the congruence subgroup kernel with the
             fundamental group of the reductive Borel-Serre
             compactification of <nobr>&Gamma;&thinsp;\&thinsp;<i>X</i></nobr>
             for certain sufficiently small <i>S</i>-arithmetic subgroups
             &Gamma; of <b>G</b>. Our result follows from explicit
             computations of the fundamental group of the reductive
             Borel-Serre compactifications of <nobr>&Gamma;&thinsp;\&thinsp;<i>X</i></nobr>.
             In the case that &Gamma; is neat, we show that this
             fundamental group is isomorphic to <nobr>&Gamma;&thinsp;/&thinsp;<i>E</i>&Gamma;</nobr>,
             where <i>E</i>&Gamma; is the subgroup generated by the
             elements of &Gamma; belonging to unipotent radicals of
             parabolic <i>k</i>-subgroups. Similar computations of the
             fundamental group of the Satake compactifications are
             made.},
   Key = {fds213234}
}

 

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