Totally acyclic complexes over noetherian schemes
By Daniel Murfet, Shokrollah Salarian. 2009
77 citations recorded by the source corpus.
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 Jorgensen's proof of the existence of Gorenstein projective precovers.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/df636c922f68411da099d4beca97f80a5a24c17b
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In Geometry and Topology
- L. Christensen
- Henrik Holm
- H. Foxby
- Greg Stevenson
- Sean Sather-Wagstaff
- S. Iyengar
- D. White
- Driss Bennis
In Statistical and Nonlinear Physics
- H. Foxby
- Henrik Holm
- L. Christensen
- Greg Stevenson
- Sean Sather-Wagstaff
- D. White
- Driss Bennis
- Tirdad Sharif
Citations in the corpus
- Beyond totally reflexive modules and back (2008, background): “For an important class of rings, Jørgensen [78] and Murfet and Salarian [85] prove existence of Gorenstein projective precovers for all modules: Theorem 5.7.”
- The direct limit closure of perfect complexes (2013, background): “In [3] such complexes are called categorically flat, in [8] they are called flat, and in [16] they are called pure acyclic.”
- Subcategories of singularity categories via tensor actions (2011, background): “In particular it has a dualising complex so by [35] (Proposition 6.”