Minimal complexes of cotorsion flat modules
P Thompson - arXiv preprint arXiv:1702.02985, 2017 - arxiv.org
arXiv preprint arXiv:1702.02985, 2017•arxiv.org
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 …
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 …
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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