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Local cohomology

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Fields Medal — Peter Scholze — ICM2018

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Relating Topology and Geometry - 2 Minute Math with Jacob Lurie

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Homologische Algebra: Kettenkomplexe und Homologiegruppen

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Reel Olivier Pilloni

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Manifolds - Smooth

In algebraic geometry, local cohomology is an analog of relative cohomology. Alexander Grothendieck introduced it in seminars in Harvard in 1961 written up by Hartshorne (1967), and in 1961-2 at IHES written up as SGA2 - Grothendieck (1968), republished as Grothendieck (2005).
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    • Definition 

    • Basic properties 

    • Relation to invariants of modules 

    • Local duality 

    • Applications