Deriving Milnor's theorem on pullback rings

2020/04/13 by Chen, Xiao-Wu, Le, Jue
#FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2004.05899

Abstract

The classical theorem of Milnor on pullback rings states that the category of projective modules over a pullback ring is equivalent to a certain category of gluing triples consisting of projective modules. We prove an analogous result on the level of derived categories, where the equivalence has to be replaced by an epivalence.

Related

• Non-surjective Milnor patching diagrams
• Separated presentations of modules over pullback rings
• Topological and algebraic pullback functors
• Pushouts and e-Projective Semimodules
• Milnor squares of algebras, I: derived equivalences