Homological and Homotopical Aspects of Torsion Theories

By Apostolos Beligiannis, I. Reiten. 2007

521 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a8f0a5d62f17b0c03106f6fb3a978dc89dd01b7d

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Citations in the corpus

Cotorsion torsion triples and the representation theory of filtered hierarchical clustering (2019, background): “In particular, rep k ( ~ Am ⊗ ~ An) contains finitely many indecomposables precisely in the cases • m ≤ 2 or n ≤ 2, • (m,n) ∈ {(3, 3), (3, 4), (3, 5), (4, 3), (5, 3)}.”
Stability conditions, torsion theories and tilting (2009, background): “First, a bounded t-structure is completely determined by its heart A; the t-structure is recovered as 〈A,A[1],A[2], . . .〉.”
On compactly generated torsion pairs and the classification of co--structures for commutative noetherian rings (2012, background): “An interesting phenomenon noticed by Bondarko [17] and Pauksztello [57, 58] is that t-structures and co-t-structures sometimes come in adjacent pairs, which can be viewed as an “unstable” version of recollements (or torsion torsion-free triples in the language of [11]).”
Gorenstein Homological Algebra of Artin Algebras (2017, background): “This report may be viewed as a preparation for reading the beautiful theory of virtually Gorenstein algebras developed in [15, 12, 13, 14].”
Gorenstein derived categories (2010, methodology): “We refer to [B] and [BR] for some properties of this class of algebras, and to [Chen] and [LZ1] for the criteria of CM-finiteness of Gorenstein Aritn algebras.”
On exact categories and applications to triangulated adjoints and model structures (2010, background): “3] and [42, §6] (we also refer to [24, 5] and [48, Chapter 9] for more information on the notions):”
Discreteness of silting objects and t ‐structures in triangulated categories (2017, background): “In recent years the connection between silting theory and the theory of t-structures (and co-t-structures) has received much attention [4, 7, 14, 16, 38, 55, 62], and silting theory has been playing an increasingly important role in the study of triangulated categories of algebraic origin, due to su”
Good tilting modules and recollements of derived module categories (2010, methodology): “[13] A torsion torsionfree triple, or TTF triple for short, i n D is a triple (X ,Y ,Z ) of full subcategoriesX ,Y andZ of D such that both(X ,Y ) and(Y ,Z ) are torsion pairs.”
Parametrizing recollement data for triangulated categories (2009, background): “The notion of t-structure is the analogue of the notion of torsion pair [10,46,4] for abelian categories.”
Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements (2014, methodology): “entually homological isomorphism in Corollary 3.12. The results of this section are used in Section 4 and Section 7. In Section 4, we study Gorenstein categories, introduced by Beligiannis and Reiten [9]. Assuming that we have an eventually homological isomorphism f: D −→F between abelian categories”
Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes (2013, unknown): “In particular, for s ∈ S, there is a distinguished triangle s → u → u(1) → Σs (7) Applying F we obtain an exact sequence”