Cofiniteness of generalized local cohomology modules for ideals of small dimension

2022/08/23 by Xiaoyan Yang, Yang, Xiaoyan, Jiaojiao Lu +1
Mathematics · #13D45 #13E05 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2208.10772

openalex publication_date 2022/08/23 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28

Abstract

Let \mathfraka be an ideal of a commutative noetherian ring R and M, N two finitely generated R-modules. By using a spectral sequence argument, it is shown that if either dim_RM≤2 and Hⁱ_\mathfraka(N) are \mathfraka-cofinite for all i≥0, or Hⁱ_\mathfraka(N) is an \mathfraka-cofinite module of dimension ≤1 for each i≥1, or q(\mathfraka,R)≤1, then the R-modules H^t_\mathfraka(M,N) are \mathfraka-cofinite for all t≥0.

Related

• Modules cofinite with respect to ideals of small dimensions
• Cofiniteness of generalized local cohomology modules
• Cofiniteness of local cohomology modules for ideals of dimension one
• Some results on local cohomology modules
• Cofiniteness and finiteness of associated prime ideals of generalized local cohomology modules