Minimal complexes of cotorsion flat modules

• Peder Thompson ^[1]
  1. [1] Texas Tech University

     Texas Tech University

     Estados Unidos

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 124, Nº 1, 2019, págs. 15-33
• Idioma: inglés
• DOI: 10.7146/math.scand.a-110787
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.