Homotopy categories of totally acyclic complexes with applications to the flat–cotorsion theory

Lars Winther Christensen, Sergio Estrada, Peder Thompson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We introduce a notion of total acyclicity associated to a subcat-egory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to the homotopy category of totally acyclic complexes. Applied to the flat–cotorsion theory over a coherent ring, this provides a new description of the category of cotorsion Gorenstein flat modules; one that puts it on equal footing with the category of Gorenstein projective modules.

Original languageEnglish
Pages (from-to)99-118
Number of pages20
JournalContemporary Mathematics
Volume751
DOIs
StatePublished - 2020

Keywords

  • Cotorsion pair
  • Gorenstein object
  • Stable category
  • Totally acyclic complex

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