Totally acyclic complexes over noetherian schemes
Daniel Murfet, Shokrollah Salarian
| Number | 52 |
|---|---|
| Author | Daniel Murfet |
| Project | C01 |
| Year | 2009 |
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.
