Geometric characterization of flat modules

Published 27 Sep 2016 in math.AG and math.AC | (1609.08327v5)

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.

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