Local cohomology modules with nonclosed support

2026/07/30 by Bhargav Bhatt, Linquan Ma
Mathematics · #math.AC #math.AG

paper · pdf

16 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We construct noetherian rings admitting local cohomology modules with nonclosed support, or equivalently with infinitely many minimal primes; this answers a question of Huneke--Lyubeznik.

Citations

• Koszul cohomology and support of local cohomology modules of complete intersections
• Lim Cohen-Macaulay sequences of modules
• A formalism of F-modules for rings with complete local finite F-representation type
• Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension
• On the associated primes of local cohomology
• The support of local cohomology modules
• Good moduli spaces for Artin stacks
• 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

Related

• Associated primes of local cohomology modules
• Local cohomology based on a nonclosed support defined by a pair of ideals
• An example of an infinite set of associated primes of a local cohomology module
• The support of local cohomology modules
• Some properties of top graded local cohomology modules