Totally acyclic complexes over noetherian schemes - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: We define a notion of total acyclicity for complexes of flat quasi-coherentsheaves over a semi-separated noetherian scheme, generalising complete flatresolutions over a ring. By studying these complexes as objects of the purederived category of flat sheaves we extend several results about totallyacyclic complexes of projective modules to schemes; for example, we prove thata scheme is Gorenstein if and only if every acyclic complex of flat sheaves istotally acyclic. Our formalism also removes the need for a dualising complex inseveral known results for rings, including Jorgensen-s proof of the existenceof Gorenstein projective precovers.



Author: Daniel Murfet, Shokrollah Salarian

Source: https://arxiv.org/



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