Semi-dualizing complexes and their Auslander categories

By L. Christensen. 2001

232 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/f4bf499781112e21ce661a1543c21906d67f874f

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Citations in the corpus

Semi-dualizing modules and related Gorenstein homological dimensions (2004, background): “For any semi-dualizing module (in fact, complex) C over A, and any complex Z with bounded and finitely generated homology, Christensen [3] introduced the dimension GdimC Z, and developed a satisfactory theory for this new invariant.”
Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras (2005, unknown): “3 it follows easily that a bounded complex X• lies in the strict image of D(iCM) iff the canonical mapδX• :X• → RHomΛ(D(Λ),X•⊗LΛ D(Λ)) is invertible, see also [30].”
Reflexivity and rigidity for complexes, I: Commutative rings (2009, background): “When Spec R is connected and M is non-zero and C-rigid, with C-rigidifying isomorphism µ, there exists a unique isomorphism α : C −→∼ M making the following diagram commute: C RHomR(χ C ,C)−1 // α RHomR(RHomR(C, C), C) RHomR(RHomR(α,C), α) M µ // RHomR(RHomR(M, C), M) Semidualizing complexes, identi”
Comparison of relative cohomology theories with respect to semidualizing modules (2007, background): “Over a noetherian ring, the next categories were introduced by Avramov and Foxby [6] when C is dualizing, and by Christensen [11] for arbitrary C .”
The set of semidualizing complexes is a nontrivial metric space (2004, background): “Both authors thank Luchezar Avramov, Lars Winther Christensen, E. Graham Evans Jr., Hans-Bjørn Foxby, Alexander Gerko, Phillip Griffith, Henrik Holm, Srikanth Iyengar, and Paul Roberts for stimulating conversations and helpful comments about this research, and the anonymous referee for improving the”
Beyond totally reflexive modules and back (2008, background): “Generalized notions of G-dimension—based on reflexivity with respect to semidualizing modules and complexes—are studied by Avramov, Iyengar, and Lipman [18], Christensen [29], Frankild and Sather-Wagstaff [60], Gerko [61], Golod [62], Holm and Jørgensen [70], by Salarian, Sather-Wagstaff, and Yassem”
Homological invariants associated to semi-dualizing bimodules (2005, methodology): “The key role will be played by semi-dualizing bimodules, which we introduce in this paper to generalize semi-dualizing modules in the sense of Christensen [5].”