Abstract local cohomology functors

2010/01/06 by Yuji Yoshino, Yoshino, Yuji, Takeshi Yoshizawa +1 · 1 citation
Mathematics · #13D09 #13D45 #Adjoint functors #Algebraic structures and combinatorial models #Category Theory (math.CT) #Cohomology #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #De Rham cohomology #Derived functor #Equivariant cohomology #Exact functor #Ext functor #FOS: Mathematics #Finitely-generated abelian group #Functor #Functor category #Grothendieck topology #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Ideal (ethics) #Local cohomology #Mathematics #Motivic cohomology #Pure mathematics #Sheaf cohomology #math.AC #math.CT #msc:13D09 #msc:13D45

paper · pdf · doi:10.48550/arxiv.1001.0862

To appear in Mathematical Journal of Okayama University

arxiv created 2010/01/06 · openalex publication_date 2010/01/06 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose to define the notion of abstract local cohomology functors. The derived functors of the ordinary local cohomology functor with support in the closed subset defined by an ideal and the generalized local cohomology functor associated with a given pair of ideals are characterized as elements of the set of all the abstract local cohomology functors.

Cited by

• On localizing subcategories of derived categories of categories of quasi-coherent sheaves on Noetherian algebraic spaces

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