Geometric characterization of flat modules

Abstract

Let $R$ be a commutative ring. Roughly speaking, we prove that an $R$-module $M$ is flat iff it is a direct limit of $R$-module affine algebraic varieties, and $M$ is a flat Mittag-Leffler module iff it is the union of its $R$-submodule affine algebraic varieties.

27 pages

References in corpus (1)

• Flat SML modules and reflexive functors

Cited by in corpus (2)

• Flat SML modules and reflexive functors
• Functorial characterization of Mittag-Leffler modules