F-injectivity does not imply F-fullness in normal domains

2025/05/31 by Alessandro De Stefani, De Stefani, Alessandro, Thomas Polstra +3
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2506.00646

openalex publication_date 2025/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are F-injective but not F-full. Along the way, we find examples of two-dimensional local geometrically normal domains which are F-injective but not F-anti-nilpotent. A crucial theme of our constructions is the behavior of F-injectivity along a purely inseparable finite base change.

Citations

• Flat morphisms with regular fibers do not preserve F-rationality
• Deformations of log canonical and F-pure singularities
• Cohomologically full rings
• Frobenius actions on local cohomology modules and deformation
• Deformation of F-injectivity and local cohomology
• Finiteness properties of local cohomology for F-pure local rings
• Local cohomology and F-stability
• The Frobenius Structure of Local Cohomology
• Extension of weakly and strongly F-regular rings by flat maps
• Deformation of F-purity and F-regularity

Related

• Regularity and finite injective dimension in characteristic p>0
• One-dimensional bad Noetherian domains
• Excellent Normal Local Domains and Extensions of Krull Domains
• On injectivity of maps between Grothendieck groups induced by completion
• F-injectivity and Buchsbaum singularities