Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings

2025/06/21 by Ryotaro Hanyu, Hanyu, Ryotaro
Computer Science · Mathematics · #13A15 #13D45 #13F05 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2506.17586

openalex publication_date 2025/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We investigate the finiteness of the set of associated primes for local cohomology modules H_Iⁱ(J) of an ideal J generated by an R-sequence, through the comparison of H_I^d+1(J) and H_I^d(R/J), where d = depth_I(R). The properties of almost factorial rings play a key role in enabling this comparison. Under suitable conditions, we prove that the finiteness of Ass H_I^d+1(J) is equivalent to that of Ass H_I^d(R/J). Moreover, we give a few conditions under which the finiteness of Ass H_Iⁱ(J) holds for all i.

Citations

• The local cohomology of a parameter ideal with respect to an arbitrary\n ideal
• Associated primes of local cohomology modules and of Frobenius powers
• An example of an infinite set of associated primes of a local cohomology module

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