Journal article

Totally acyclic complexes over noetherian schemes

Daniel Murfet, Shokrollah Salarian

ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2011

Abstract

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-separated noetherian scheme, and study these complexes using the pure derived category of flat quasi-coherent sheaves. We prove that a scheme is Gorenstein if and only if every acyclic complex of flat quasi-coherent sheaves is totally acyclic. Our formalism also removes the need for a dualising complex in several known results for rings, including Jørgensen's proof of the existence of Gorenstein projective precovers. © 2010 Elsevier Inc.

University of Melbourne Researchers

Grants

Awarded by University of Isfahan


Funding Acknowledgements

This project was initiated in June 2007, while the second author was visiting at the Australian National University. We thank the ANU, and in particular Professor Neeman, for providing a stimulating research environment. The first author thanks Srikanth Iyengar, Henning Krause and Xiao-Wu Chen for discussions relating to this work. The work of the second author has been supported by a grant from the University of Isfahan (No. 861125). He also would like to thank the Center of Excellence for Mathematics (University of Isfahan).