Minimal complexes of cotorsion flat modules
Journal article, Peer reviewed
Accepted version
![Thumbnail](/ntnu-xmlui/bitstream/handle/11250/2638499/5.%2bminimal%2bcomplexes%2bof%2bcotorsion%2bflat%2bmodules%2b20181121arxiv.pdf.jpg?sequence=5&isAllowed=y)
Åpne
Permanent lenke
http://hdl.handle.net/11250/2638499Utgivelsesdato
2019Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2438]
- Publikasjoner fra CRIStin - NTNU [38034]
Sammendrag
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.