Totally acyclic complexes over noetherian schemes

Details Totally acyclic complexes over noetherian schemes Totally acyclic complexes over noetherian schemes

2009-02-17

arxiv.org/abs/0902.3013v1

Mathematics

Algebraic Geometry

37 pages, comments welcome

Scientific paper

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.

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