Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory
Peer reviewed, Journal article
Accepted version
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Date
2019Metadata
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- Institutt for matematiske fag [2438]
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Original version
http://dx.doi.org/10.1090/conm/751/15112Abstract
We introduce a notion of total acyclicity associated to a subcategory 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.