About: Verdier duality

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In mathematics, Verdier duality is a cohomological duality in algebraic topology that generalizes Poincaré duality for manifolds. Verdier duality was introduced in 1965 by Jean-Louis Verdier as an analog for locally compact topological spaces of Alexander Grothendieck's theory ofPoincaré duality in étale cohomologyfor schemes in algebraic geometry. It is thus (together with the said étale theory and for example Grothendieck's coherent duality) one instance of Grothendieck's six operations formalism.

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  • In mathematics, Verdier duality is a cohomological duality in algebraic topology that generalizes Poincaré duality for manifolds. Verdier duality was introduced in 1965 by Jean-Louis Verdier as an analog for locally compact topological spaces of Alexander Grothendieck's theory ofPoincaré duality in étale cohomologyfor schemes in algebraic geometry. It is thus (together with the said étale theory and for example Grothendieck's coherent duality) one instance of Grothendieck's six operations formalism. Verdier duality generalises the classical Poincaré duality of manifolds in two directions: it applies to continuous maps from one space to another (reducing to the classical case for the unique map from a manifold to a one-point space), and it applies to spaces that fail to be manifolds due to the presence of singularities. It is commonly encountered when studying constructible or perverse sheaves. (en)
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  • Jean-Louis Verdier (en)
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  • Jean-Louis (en)
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  • Verdier (en)
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  • 1995 (xsd:integer)
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  • In mathematics, Verdier duality is a cohomological duality in algebraic topology that generalizes Poincaré duality for manifolds. Verdier duality was introduced in 1965 by Jean-Louis Verdier as an analog for locally compact topological spaces of Alexander Grothendieck's theory ofPoincaré duality in étale cohomologyfor schemes in algebraic geometry. It is thus (together with the said étale theory and for example Grothendieck's coherent duality) one instance of Grothendieck's six operations formalism. (en)
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  • Verdier duality (en)
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