Totally acyclic complexes over noetherian schemes

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We 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.
37 pages, comments welcome

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Algebraic Geometry, Commutative Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/220417

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.3013
 http://arxiv.org/abs/0902.3013

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arXiv