Flat epimorphisms and silting epimorphisms coincide for commutative rings

2025/10/03 by Jan Šťovíček, Šťovíček, Jan
Mathematics · #13B40 (Primary) #16D40 #16S90 (Secondary) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2510.03440

openalex publication_date 2025/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the relation between partial silting modules, Gabriel topologies, and ring epimorphisms, with a particular emphasis on commutative rings. We show that a ring epimorphism of commutative rings is flat if and only if it is a silting ring epimorphism.

Citations

• Abelian right perpendicular subcategories in module categories
• Silting and cosilting classes in derived categories
• Silting modules over commutative rings
• Silting modules and ring epimorphisms
• Silting modules
• Tilting Modules over Tame Hereditary Algebras
• Tilting modules and universal localization
• Tilting modules arising from ring epimorphisms

Related

• Silting modules and ring epimorphisms
• Silting modules over commutative rings
• On flat epimorphisms of rings and pointwise localizations
• Minimal silting modules and ring extensions
• On finite type epimorphisms of rings