2015/01/19 by V. H. Jorge Pérez, V. H. Jorge Perez, T. H. Freitas +2
Mathematics · #13D45 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13D45
paper · pdf · doi:10.48550/arxiv.1501.04464
arxiv created 2015/01/19 · openalex publication_date 2015/01/19 · arxiv updated 2015/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let (R,\mathfrakm,k) denote a local ring. For I and J ideals of R, for all integer i, let HiI,J(-) denote the i-th local cohomology functor with respect to (I,J). Here we give a generalized version of Local Duality Theorem for local cohomology defined by a pair of ideals. Also, for M be a finitely generated R-module, we study the behavior of the endomorphism rings HtI,J(M) and D(HtI,J(M)) where t is the smallest integer such that the local cohomology with respect to a pair of ideals is non-zero and D(-):= \rm HomR(-,ER(k)) is the Matlis dual functor. We show too that if R be a d-dimensional complete Cohen-Macaulay and HiI,J(R)=0 for all i≠ t, the natural homomorphism R→ \rm HomR(HtI,J(KR), HtI,J(KR)) is an isomorphism and for all i≠ t, where KR denote the canonical module of R.