Perverse Sheaves

@article{Maxim2019PerverseS,
  title={Perverse Sheaves},
  author={Laurenţiu Maxim},
  journal={Graduate Texts in Mathematics},
  year={2019}
}
  • L. Maxim
  • Published 2019
  • Mathematics
  • Graduate Texts in Mathematics
View via Publisher
47 Citations
Highly Influential Citations
2
Background Citations
10
Methods Citations
3

47 Citations

Citation Type

Citation Type

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Equivalent definitions of Arthur packets for real quasisplit unitary groups
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A generalization of the b-function lemma
  • S. Raskin
  • Mathematics
    Compositio Mathematica
  • 2021
We establish some cohomological bounds in $D$-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the $b$-function lemma for…
Absolute sets of rigid local systems
The absolute sets of local systems on a smooth complex algebraic variety are the subject of a conjecture of [BW] based on an analogy with special subvarieties of Shimura varieties. An absolute set…
Borel-Moore homology of determinantal varieties
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Estimates for zero loci of Bernstein-Sato ideals
We give estimates for the zero loci of Bernstein-Sato ideals. An upper bound is proved as a multivariate generalisation of the upper bound by Lichtin for the roots of Bernstein-Sato polynomials. The…
Generic Vanishing, 1-forms, and Topology of Albanese Maps
The goal of this article is to study global holomorphic 1-forms on smooth projective varieties. First, we establish an interesting link between the generic vanishing theory and the topology of the…
Generic vanishing and holomorphic 1-forms
The goal of this article is three-fold; first we establish an interesting link between some sets related to cohomologies of complex local systems and the stratification of the Albanese morphism of…
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References

SHOWING 1-10 OF 10 REFERENCES
The decomposition theorem, perverse sheaves and the topology of algebraic maps
We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the…
D-Modules, Perverse Sheaves, and Representation Theory
D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular Holonomic…
The Development of Intersection Homology Theory
58 pages, hypertext links added; appeared in Part 3 of the special issue of Pure and Applied Mathematics Quarterly in honor of Robert MacPherson. However, the flags in the margin were unfortunately…
Sheaves in Topology
1 Derived Categories.- 1.1 Categories of Complexes C*(A).- 1.2 Homotopical Categories K*(A).- 1.3 The Derived Categories D*(A).- 1.4 The Derived Functors of Hom.- 2 Derived Categories in Topology.-…
Morse theory for constructible sheaves
In this chapter we prove the basic results about stratified Morse theory in the framework of constructible sheaves. We follow the notions of Goresky-MacPherson so that one can easily compare our…
Singularities and Topology of Hypersurfaces
This book systematically presents a large number of basic results on the topology of complex algebraic varieties using the information on the local topology and geometry of a singularity. These…
The Riemann-Hilbert Problem for Holonomic Systems
On demontre l'equivalence de la categorie derivee des systemes holonomes et celle des faisceaux constructibles
Intersection homology II
In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is a…
Sur le problème de Hilbert-Riemann
Lokale topologische Eigenschaften komplexer Räume