Classes of Flat Modules Arising in Algebraic Geometry and Approximations

Abstract

Abstract Locally projective (i.e., flat Mittag-Leffler) modules are known to provide for approximations only over perfect rings. Recently, very flat modules were introduced by Positselski in his study of contraherent cosheaves on a scheme X.

For X=Spec(R) X=Spec(R) , where R is a Noetherian domain, we show that locally very flat modules provide for approximations only if X is finite.

Keywords

• Classes
• Flat
• Modules
• Arising
• Algebraic
• Geometry
• Approximations