Cohomologically complete intersections with vanishing of Betti numbers

2014/07/02 by Waqas Mahmood, Mahmood, Waqas
Mathematics · #13D45 #Advanced Combinatorial Mathematics #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.1407.0472

submitted

arxiv created 2014/07/02 · openalex publication_date 2014/07/02 · arxiv updated 2014/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be ideal of an n-dimensional local Gorenstein ring R. In this paper we will describe several necessary and sufficient conditions such that the ideal I becomes cohomologically complete intersections. In fact, as a technical tool, it will be shown that the vanishing Hⁱ_I(R)= 0 for all i≠ c= \grade (I) is equivalent to the vanishing of the Betti numbers of H^c_I(R). This gives a new characterization to check the cohomologically complete intersections property with the homological properties of the vanishing of Tor modules of H^c_I(R).

Citations

• On Endomorphism Rings of Local Cohomology Modules

Related

• On cohomologically complete intersections
• On Cohomologically Complete Intersections in Cohen-Macaulay Rings
• Extremal growth of Betti numbers and trivial vanishing of (co)homology
• On vanishing of generalized local cohomology modules
• Generalized local cohomology modules and homological Gorenstein dimensions