2007/08/03 by Florian Enescu, Melvin Hochster, Enescu, Florian +1 · 1 citation
Mathematics · #13A35 #13D45 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13A35 #msc:13D45
paper · pdf · doi:10.48550/arxiv.0708.0553
35 pages. Section 3 was revised to emphasize Theorem 3.1, and some minor corrections/changes were performed. To appear in Algebra and Number Theory
openalex publication_date 2007/08/03 · arxiv created 2008/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a local ring of positive prime characteristic there is a natural Frobenius action on its local cohomology modules with support at its maximal ideal. In this paper we study the local rings for which the local cohomology modules have only finitely many submodules invariant under the Frobenius action. In particular we prove that F-pure Gorenstein local rings as well as the face ring of a finite simplicial complex localized or completed at its homogeneous maximal ideal have this property. We also introduce the notion of an anti-nilpotent Frobenius action on an Artinian module over a local ring and use it to study those rings for which the lattice of submodules of the local cohomology that are invariant under Frobenius satisfies the Ascending Chain Condition.