Totally acyclic complexes over noetherian schemes

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dc.creatorMurfet, Daniel
dc.creatorSalarian, Shokrollah
dc.date2009-02-17
dc.date.accessioned2026-07-07T12:43:26Z
dc.date.available2026-07-07T12:43:26Z
dc.descriptionWe define a notion of total acyclicity for complexes of flat quasi-coherent sheaves over a semi-separated noetherian scheme, generalising complete flat resolutions over a ring. By studying these complexes as objects of the pure derived category of flat sheaves we extend several results about totally acyclic complexes of projective modules to schemes; for example, we prove that a scheme is Gorenstein if and only if every acyclic complex of flat sheaves is totally acyclic. Our formalism also removes the need for a dualising complex in several known results for rings, including Jorgensen's proof of the existence of Gorenstein projective precovers.
dc.description37 pages, comments welcome
dc.identifierhttps://arxiv.org/abs/0902.3013
dc.identifierhttp://arxiv.org/abs/0902.3013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220417
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.titleTotally acyclic complexes over noetherian schemes
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