Flat Covers in the Category of Quasi-coherent Sheaves Over the Projective Line

By Edgar E. Enochs, Sergio Estrada, J. R. G. Rozas, Luis Oyonarte. 2004

46 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4dc47716f2cd38e368af2f7bb67bb8d8ea661205

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Kaplansky classes and derived categories (2007, background): “See [4, 8 ,9,11,12]. In each category mentioned above, Enochs and coauthors have essentially shown that the class of flat objects form a Kaplansky class.”
Covers in finitely accessible categories (2010, methodology): “We point out the work of Aldrich, Enochs, Garćıa Rozas and Oyonarte [2] and El Bashir [14] in arbitrary Grothendieck categories, Enochs, Estrada, Garćıa Rozas and Oyonarte for quasi-coherent sheaves over the projective line [16] and for quasi-coherent sheaves over a scheme [17], Enochs and Oyonarte ”
Ideal approximation theory (2013, methodology): “Expositions of approximation theory for categories of modules may be found in the monographs of Beligiannis and Reiten [4] and Göbel and Trlifaj [17], but cotorsion pairs have also been used to study approximation theory in sheaf categories [13], general Grothendieck categories [15,20], and more abs”
The phantom cover of a module (2007, background): “Proof. By [ 14, Theorem 2.7 ] or [18, Theorem 11], the torsion subobject tR(− ,N) of (− ,N) has a flat cover η : (− ,M) → tR(− ,N) in the category ((R-mod)op, Ab).”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, background): “hold also for sheaf categories, for instance in [17, 18, 19].”
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, 11, 12], a fact which Gillespie [18] and Hovey [23] later applied in a crucial way to constructing monoidal model structures for complexes of sh”