Kaplansky classes and derived categories

By James Gillespie. 2007

103 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4a167636928c881d37c3a7ea4fe85f7ac1443926

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Citations in the corpus

Almost free modules and Mittag-Leffler conditions (2009, methodology): “Recall that a positive answer to question (2) is known when D is replaced by the class of all projective modules (in case X is the projective line), and by the class of all flat modules (in case X is quasi–compact and semi–separated), see [13] and [20], respectively.”
Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves (2013, methodology): “In this context, we denote for brevity Cac(A) by Ã (this notation has been used by Gillespie in [27, 28, 29]).”
Cotorsion pairs and model structures on Ch(R) (2011, background): “The cofibrantly generated property is very important for a model structure and is studied in [18,19,21].”
Deconstructibility and the Hill Lemma in Grothendieck categories (2010, methodology): “Our exposition here uses ideas of Gillespie from [16, §3], which were also nicely presented by Hovey in [23, §7].”
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”
Model structures on exact categories (2010, background): “at model structure on chain complexes of R-modules constructed in [Gil04], or chain complexes sheaves [Gil06], or chain complexes of quasicoherent sheaves on a quasi-compact and semi-separated scheme [Gil07]. With this model structure Proposition 4.3 says two chain maps f,g: X → Y are right homotopi”
On exact categories and applications to triangulated adjoints and model structures (2010, methodology): “The proof for case (2) is inspired by [20], while a similar argument is also used in the proof of [16, Lemma 4.”
Model category structures arising from Drinfeld vector bundles (2009, methodology): “Moreover, the methods of [14] depend heavily on the fact that the class of all flat modules is closed under direct limits.”
Hereditary abelian model categories (2015, background): “3 was for the construction of the flat model structure on chain complexes of (quasi-coherent) sheaves [25].”