Koszul cohomology and support of local cohomology modules of complete intersections

2025/09/26 by Michael Gintz, Gintz, Michael, Wenliang Zhang +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.22988

openalex publication_date 2025/09/26 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

Let R be a noetherian commutative ring and f₁,…,f_c be a regular sequence in R. We introduce a framework to study Supp(H^j_I(R/(f₁,…,f_c))) by linking the Koszul cohomology of H^j_I(R) on the sequence f₁,…,f_c and local cohomology modules H^j_I(R/(f₁,…,f_c)). As an application, we prove that if R is a noetherian regular ring of prime characteristic p and f₁,f₂ form a regular sequence in R then Supp(H^j_I(R/(f₁,f₂))) is Zariski-closed for each integer j and each ideal I.

Citations

• The support of local cohomology modules
• Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2)
• Associated primes of local cohomology module
• Associated primes of local cohomology modules and of Frobenius powers
• p-torsion elements in local cohomology modules
• An example of an infinite set of associated primes of a local cohomology module

Cited by

• Local cohomology modules with nonclosed support

Related

• Regular sequences and local cohomology modules with respect to a pair of ideals
• Filter regular sequences and generalized local cohomology modules
• Some results on the local cohomology modules with respect to a pair of ideals
• On the regularity and Koszulness of modules over local rings
• Cohomological supports over derived complete intersections and local\n rings