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Acyclicity of Complexes of Flat Modules
Published online by Cambridge University Press: 11 January 2016
Abstract
Let R be a noetherian commutative ring, and
a complex of flat R-modules. We prove that if is acyclic for every ρ ϵ Spec R, then
is acyclic, and H0(
) is R-flat. It follows that if
is a (possibly unbounded) complex of flat R-modules and
is exact for every ρ ϵ Spec R, then
is exact for every R-complex
. If, moreover,
is a complex of projective R-modules, then it is null-homotopic (follows from Neeman’s theorem).
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2008
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