Noetherian hereditary abelian categories satisfying Serre duality

By I. Reiten, Michel van den Bergh. 2002

335 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36030f5df4d259fb4fd64a33c84630e5eb893cf5

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Citations in the corpus

Auslander–Reiten translations in monomorphism categories (2011, background): “ Tn(A)-modules, and hence the stable monomorphism category Sn(A) is a Hom-ﬁnite Krull-Schmidt triangulated category with Auslander-Reiten triangles. By Theorem I.2.4 of I. Reiten and M. Van den Bergh [RV], Sn(A) has a Serre functor FS. We study the periodicity of FS on the objects of Sn(A) (Theorem ”
The stable Calabi-Yau dimension of tame symmetric algebras (2006, background): “Moreover, if F and F ′ are two Serre functors of A , then they are naturally isomorphic (see [11], [40]).”
On the cluster category of a marked surface without punctures (2010, background): “Moreover, since C is 2-Calabi-Yau, C has AR-triangles and the AR-translation is given by τ = [1] (see [26]).”
Calabi–Yau triangulated categories (2008, background): “The equivalence between (i) and (ii) is proved in [ 50 ] and the equivalence between (ii) and (iii) in [26].”
Projective-injective modules, Serre functors and symmetric algebras (2005, background): “Two right Serre functors are isomorphic (see [55], Lemma I.”
An Auslander-Type result for Gorenstein-projective modules (2007, methodology): “Hence the triangulated category A-Gproj has Auslander-Reiten triangles, and by a theorem of Reiten-Van den Bergh ([25], Theorem I.”
Auslander-Gorenstein algebras and precluster tilting (2016, background): “(b) Since U(C) has a Serre functor, it has almost split triangles [37].”
The Mukai pairing, I: the Hochschild structure (2003, background): “To construct the map Φ∗ : HHi(X) → HHi(Y ) we would want to take the adjoint of Φ † (recall that homology is thought of as the dual of Nat(1Y , SY ) with respect to Serre duality of natural transformations).”
Mutation in triangulated categories and rigid Cohen–Macaulay modules (2006, background): “Definition 2.8 Following Bondal and Kapranov [24] (see also [ 56 ]), we call a k-linear autofunctor S : T → T a Serre functor of T if there exists a functorial isomorphism”