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The stable category of Gorenstein flat sheaves on a noetherian scheme

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arxiv 1904.07661 v2 pith:LSFGJLN7 submitted 2019-04-16 math.AC math.AG

Lars Winther Christensen , Sergio Estrada , Peder Thompson This is my paper · ORCID
classification math.ACmath.AG
keywords categoryflatgorensteinnoetheriansheavesacyclicanaloguecomplexes
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For a semi-separated noetherian scheme, we show that the category of cotorsion Gorenstein flat quasi-coherent sheaves is Frobenius and a natural non-affine analogue of the category of Gorenstein projective modules over a noetherian ring. We show that this coheres perfectly with the work of Murfet and Salarian that identifies the pure derived category of F-totally acyclic complexes of flat quasi-coherent sheaves as the natural non-affine analogue of the homotopy category of totally acyclic complexes of projective modules.

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  1. Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity

    math.CT 2025-09 conditional novelty 7.0 of 10

    For hereditary complete cotorsion pairs generated by a set in a Grothendieck category, the coderived category of the left class is equivalent to the contraderived category of the right class, and for sandwiched pairs ...

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