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Minimal complexes of cotorsion flat modules

Thompson, Peder
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2638499
Date
2019
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  • Institutt for matematiske fag [1769]
  • Publikasjoner fra CRIStin - NTNU [26648]
Original version
Mathematica Scandinavica. 2019, 124 (1), 15-33.   10.7146/math.scand.a-110787
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.
Publisher
Mathematica Scandinavica
Journal
Mathematica Scandinavica

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