Gorenstein differential graded algebras

Jørgensen, Peter; Frankild, Anders

doi:10.1007/bf02776063

Cited by 30 publications

(35 citation statements)

References 13 publications

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“…Félix et al have considered pretty much this same extension in the topological context of rational homotopy theory and DGAs [20]; we generalize their work and have benefitted from it. Frankild and Jorgensen [21] have also studied an extension of the Gorenstein condition to DGAs, but their intentions are quite different from ours.…”

Section: Relationship To Previous Workmentioning

confidence: 89%

Duality in algebra and topology

Dwyer

Greenlees

Iyengar

2006

Advances in Mathematics

130

321

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We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson-Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross-Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.

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Section: Relationship To Previous Workmentioning

confidence: 89%

Duality in algebra and topology

Dwyer

Greenlees

Iyengar

2006

Advances in Mathematics

130

321

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“…The implication that when R is Gorenstein the k-vector space Ext R (k, R) is onedimensional was proved in [13]. The converse proves a conjecture in [13].…”

Section: Introductionmentioning

confidence: 88%

“…In a recent paper, Frankild and Jørgensen [13] proposed a new notion of 'Gorenstein' DG algebras. The natural problem arises of how their approach relates to those of Félix, Halperin and Thomas and Avramov and Foxby?…”

Section: Introductionmentioning

confidence: 99%

Dualizing Differential Graded Modules and Gorenstein Differential Graded Algebras

Frankild¹,

Iyengar²,

Jørgensen³

2003

J. London Math. Soc.

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The paper explores dualizing differential graded (DG) modules over DG algebras. The focus is on DG algebras that are commutative local, and finite. One of the main results established is that, for this class of DG algebras, a finite DG module is dualizing precisely when its Bass number is 1. As a corollary, one obtains that the Avramov–Foxby notion of Gorenstein DG algebras coincides with that due to Frankild and Jørgensen. One other key result is that, under suitable hypotheses, any two dualizing DG modules are quasiisomorphic up to a suspension. In addition, it is established that a number of naturally occurring DG algebras possess dualizing DG modules.

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“…We remark that there are various notions of Gorensteinness for differential graded algebras in the literature and recommend [8,11,13] to the interested reader. We also recall that for a simply connected Gorenstein differential graded algebra A of finite type the category D c (A) is Calabi-Yau of dimension d, i.e.…”

Section: Gorenstein Differential Graded Algebrasmentioning

confidence: 99%

Families of Auslander–Reiten components for simply connected differential graded algebras

Schmidt

2008

Math. Z.

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Peter Jørgensen introduced the Auslander-Reiten quiver of a simply connected Poincaré duality space. He showed that its components are of the form Z A ∞ and that the Auslander-Reiten quiver of a d-dimensional sphere consists of d − 1 such components. We show that this is essentially the only case where finitely many components appear. More precisely, we construct families of modules, where for each family, each module lies in a different component. Depending on the cohomology dimensions of the differential graded algebras which appear, this is either a discrete family or an n-parameter family for all n.

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Gorenstein differential graded algebras

Cited by 30 publications

References 13 publications

Duality in algebra and topology

Duality in algebra and topology

Dualizing Differential Graded Modules and Gorenstein Differential Graded Algebras

Families of Auslander–Reiten components for simply connected differential graded algebras

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