Relative homological algebra in the category of quasi-coherent sheaves

By Edgar E. Enochs, Sergio Estrada. 2005

113 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f10bc0541e6650ee213515645258638332340ee

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Citations in the corpus

Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, background): “hold also for sheaf categories, for instance in [17, 18, 19].”
Kaplansky classes and derived categories (2007, methodology): “For each x ∈ M, there corresponds some i ∈ I such that x ∈ Mi .B ut i∈I Mi is κ-filtered and |M| 9 ].”
Gorenstein categories and Tate cohomology on projective schemes (2007, methodology): “this section we will use the fact that Qco(X) over any scheme X is equivalent to the category of certain representations of some quiver Q, which may be chosen in various ways, (see [ 11, Section 2 ] or [25, 3.1] for an explanation of this viewpoint).”
Approximations and adjoints in homotopy categories (2010, background): “In [14], Enochs and Estrada have shown that quasi-coherent sheaves admit flat covers (by viewing sheaves as representations of appropriate quivers).”
Cotorsion pairs and degreewise homological model structures (2008, methodology): “Then all the hypotheses of Corollary 5.6 hold with this choice of •. We refer the reader to [Gil07] and [ EE05 ] for more details.”
Deconstructibility and the Hill Lemma in Grothendieck categories (2010, methodology): “Kaplansky classes have been explicitly or implicitly used for proving approximation properties of flat modules or sheaves in various settings [2, 7, 9, 10, 12, 13], a fact which Gillespie [18] and Hovey [23] later applied in a crucial way to constructing monoidal model structures for complexes of sh”