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2017•Taiwanese Journal of MathematicsOpen access

On the Finiteness Results of Generalized Local Cohomology Modules with Respect to a Pair of Ideals

Tran Tuan Nam, Nguyen Minh Tri

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Abstract

We study the finiteness of associated primes and support of the generalized local cohomology modules $H^i_{I,J}(M,N)$ concerning Grothendieck's conjecture and Huneke's question. The paper also discusses the relationship between the vanishing and the finiteness of the generalized local cohomology modules.

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We study the finiteness of associated primes and support of the generalized local cohomology modules $H^i_{I,J}(M,N)$ concerning Grothendieck's conjecture and Huneke's question. The paper also discusses the relationship between the vanishing and the finiteness of the generalized local cohomology modules.

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Available abstract

We study the finiteness of associated primes and support of the generalized local cohomology modules $H^i_{I,J}(M,N)$ concerning Grothendieck's conjecture and Huneke's question. The paper also discusses the relationship between the vanishing and the finiteness of the generalized local cohomology modules.

Key concepts: Mathematics, Local cohomology, Conjecture, Pure mathematics, Cohomology, Algebra over a field, Finitely-generated abelian group

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