Sheaves on Manifolds

Kashiwara, Masaki; Schapira, Pierre

doi:10.1007/978-3-662-02661-8

Cited by 934 publications

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“…We amplify and complement this crash course in the appendices in §5 and in section §2 on perverse sheaves. Standard references are [19,82,87,115,107].…”

Section: Crash Course On Sheaves and Derived Categoriesmentioning

confidence: 99%

“…The reader can consult [9,115,68]. Recall that we are dealing with Q-coefficients and with middleperversity only.…”

Section: Perverse Sheavesmentioning

confidence: 99%

“…for open and closed immersions and standard truncation. See [9], or [115]. Complete and brief summaries can be found in [52,53].…”

Section: By Verdier Duality We Havementioning

confidence: 99%

“…Standard references for what follows are [115,82,19,107,9]; see also [162]. In what follows, we freely refer to our crash-course in §1.5 and to the complete references given above.…”

Section: The Formalism Of the Constructible Derived Categorymentioning

confidence: 99%

“…Using injective resolutions and the two global sections functors Γ and Γ c we define the derived global sections functors (see [82,115] The sheaf-theoretic direct image functors f * , f ! : Sh X → Sh Y are left exact as functors, e.g.…”

Section: The Formalism Of the Constructible Derived Categorymentioning

confidence: 99%

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The decomposition theorem, perverse sheaves and the topology of algebraic maps

Andrea

Migliorini

2009

Bull. Amer. Math. Soc.

162

152

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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 theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the decomposition theorem, indicate some important applications and examples.

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“…We amplify and complement this crash course in the appendices in §5 and in section §2 on perverse sheaves. Standard references are [19,82,87,115,107].…”

Section: Crash Course On Sheaves and Derived Categoriesmentioning

confidence: 99%

“…The reader can consult [9,115,68]. Recall that we are dealing with Q-coefficients and with middleperversity only.…”

Section: Perverse Sheavesmentioning

confidence: 99%

“…for open and closed immersions and standard truncation. See [9], or [115]. Complete and brief summaries can be found in [52,53].…”

Section: By Verdier Duality We Havementioning

confidence: 99%

“…Standard references for what follows are [115,82,19,107,9]; see also [162]. In what follows, we freely refer to our crash-course in §1.5 and to the complete references given above.…”

Section: The Formalism Of the Constructible Derived Categorymentioning

confidence: 99%

Section: The Formalism Of the Constructible Derived Categorymentioning

confidence: 99%

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The decomposition theorem, perverse sheaves and the topology of algebraic maps

Andrea

Migliorini

2009

Bull. Amer. Math. Soc.

162

152

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Euler characteristics of algebraic varieties

Cappell

Maxim

Shaneson

2007

Comm Pure Appl Math

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This note studies the behavior of Euler characteristics and of intersection homology Euler characteristics under proper morphisms of algebraic (respectively, analytic) varieties. The methods also yield, for algebraic (respectively, analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck groups of constructible sheaves. Similar formulae for Hodgetheoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in [5,14].

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Hodge genera of algebraic varieties I

Cappell

Maxim

Shaneson

2007

Comm Pure Appl Math

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The aim of this paper is to study the behavior of Hodge-theoretic (intersection homology) genera and their associated characteristic classes under proper morphisms of complex algebraic varieties. We obtain formulae that relate (parametrized families of) global invariants of a complex algebraic variety X to such invariants of singularities of proper algebraic maps defined on X . Such formulae severely constrain, both topologically and analytically, the singularities of complex maps, even between smooth varieties. Similar results were announced by the first and third author in [13,32].

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Sheaves on Manifolds

Cited by 934 publications

References 0 publications

The decomposition theorem, perverse sheaves and the topology of algebraic maps

The decomposition theorem, perverse sheaves and the topology of algebraic maps

Euler characteristics of algebraic varieties

Hodge genera of algebraic varieties I

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