A new proof of the local criterion of flatness
Abstract
Let (A,mA) -> (B,mB) be a local morphism of local noetherian rings and M a finitely generated B-module. Then it follows from TorA1(M,A/mA) = 0 that M is a flat A-module. This is usually called the "local criterion of flatness". We give a proof that proceeds along different lines than the usual textbook proofs, using completions and only elementary properties of flat modules and the Tor-functor.
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