Minimal complexes of cotorsion flat modules

  • Peder Thompson

Abstract

Let $R$ be a commutative noetherian ring. We give criteria for a complex of cotorsion flat $R$-modules to be minimal, in the sense that every self homotopy equivalence is an isomorphism. To do this, we exploit Enochs' description of the structure of cotorsion flat $R$-modules. More generally, we show that any complex built from covers in every degree (or envelopes in every degree) is minimal, as well as give a partial converse to this in the context of cotorsion pairs. As an application, we show that every $R$-module is isomorphic in the derived category over $R$ to a minimal semi-flat complex of cotorsion flat $R$-modules.

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Published
2019-01-13
How to Cite
Thompson, P. (2019). Minimal complexes of cotorsion flat modules. MATHEMATICA SCANDINAVICA, 124(1), 15-33. https://doi.org/10.7146/math.scand.a-110787
Section
Articles