Smashing subcategories and the telescope conjecture – an algebraic approach

By Henning Krause. 2000

216 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/8318de7525e5b89d08446c09f0fda4ba13a51b50

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Citations in the corpus

The phantom cover of a module (2007, unknown): “For a compactly generated triangulated category T , a theory of purity has been developed independently by A. Beligiannis [4,5] and H. Krause [ 21 ].”
Silting Objects (2018, background): “The theory of purity in a compactly generated triangulated category T has been developed around 2000 in [69, 27].”
Cohomological quotients and smashing localizations (2003, methodology): “We start with descriptions of Filt I and I which we take from [20].”
Proper classes and Gorensteinness in extriangulated categories (2019, background): “[13] H. Krause, Smashing subcategories and the telescope conjecture: An algebraic approach, Invent.”
Applications of Cotorsion Pairs (2003, methodology): “The next proposition describes smashing subcategories of T in terms of the functor category (T 0 ,Ab); it is taken from [12].”
Recollements and Hochschild theory (2011, methodology): “referee showed me an elegant proof of Theorem 2 by using the correspondence between the smashing subcategories of D(A) and the idempotent ideals of the category Dc(A) of compact objects of D(A) (ref. [28, 33]). Here, we just provide a relatively elementary proof. 5 Recollements and smoothness In thi”
Parametrizing recollement data for triangulated categories (2009, background): “Krause’s parametrization [31,32] of smashing subcategories of compactly generated triangulated categories.”
A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “The conjecture is presented in this form in [38] (and it is based on conjectures by Ravenel [52, 1.”
Homological and Homotopical Aspects of Torsion Theories (2007, methodology): “Then by a result of Krause, see Theorem 4.4 in [77], it follows that Λ lies in XT , and then by Theorem 3.4 we have that T is a tilting module.”
Ideal approximation theory (2013, background): “In the stable category of a finite group ring, the theory of phantom morphisms was developed in a series of papers [16,6,7,5] by Benson and Gnacadja; the triangulated version of this notion of a phantom morphism was studied in [3,24].”
Definable Additive Categories: Purity and Model Theory (2011, unknown): “These were extended by various people, see Burke [11], Herzog [41], Krause [52], Prest [79], to more general contexts.”
Torsion pairs in silting theory (2016, unknown): “T c of contravariant additive functors from T c to Mod ( (cid:90) ) , which is known to be a locally coherent Grothendieck category (see [Krause 1997; 2000, Subsection 1.2]).”