Titlebook: Weil Conjectures, Perverse Sheaves and ℓ-adic Fourier Transform; Reinhardt Kiehl,Rainer Weissauer Book 2001 Springer-Verlag Berlin Heidelb

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The Formalism of Derived Categories,of the category .(.), the notion of (short) exact sequences of complexes no longer exists and has to be replaced by the notion of distinguished triangles, which itself derives from the concept of mapping cones.

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The Formalism of Derived Categories,of the category .(.), the notion of (short) exact sequences of complexes no longer exists and has to be replaced by the notion of distinguished triangles, which itself derives from the concept of mapping cones.

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The Formalism of Derived Categories,ory is defined by making quasiisomorphisms into isomorphisms and this allows to identify complexes with their resolutions. Recall, that a complex map .′ → . is a quasiisomorphism, if the induced cohomology morphisms ..(.’) → ..(.)are isomorphisms in all degrees. However, by taking this localization

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The Formalism of Derived Categories,ory is defined by making quasiisomorphisms into isomorphisms and this allows to identify complexes with their resolutions. Recall, that a complex map .′ → . is a quasiisomorphism, if the induced cohomology morphisms ..(.’) → ..(.)are isomorphisms in all degrees. However, by taking this localization

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Perverse Sheaves,sky-MacPherson, which originally was not defined in terms of sheaf theory but rather using explicit chain complexes. Perhaps stimulated by the Kazhdan-Lusztig conjectures it was Deligne, who gave a reformulation of the notion of intersection cohomology within the setting of sheaf theory. In this for

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