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Postnikov extensions for ring spectra
, 2006
"... We give a functorial construction of kinvariants for ring spectra, and use these to classify extensions in the Postnikov tower of a ring spectrum. ..."
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Cited by 9 (3 self)
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We give a functorial construction of kinvariants for ring spectra, and use these to classify extensions in the Postnikov tower of a ring spectrum.
ENRICHED MODEL CATEGORIES AND AN APPLICATION TO ADDITIVE ENDOMORPHISM SPECTRA
"... Abstract. We define the notion of an additive model category and prove that ..."
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Cited by 9 (3 self)
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Abstract. We define the notion of an additive model category and prove that
A curious example of two model categories and some associated differential graded algebras, in preparation
"... Abstract. The paper gives a new proof that the model categories of stable modules for the rings Z/p 2 and Z/p[ɛ]/(ɛ 2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent ..."
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Cited by 2 (1 self)
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Abstract. The paper gives a new proof that the model categories of stable modules for the rings Z/p 2 and Z/p[ɛ]/(ɛ 2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with nonisomorphic Ktheories. Contents
Local framings
"... Abstract. Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured setup studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how this is compatible with Bousfield localisation to ga ..."
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Abstract. Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured setup studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how this is compatible with Bousfield localisation to gain insight into the deeper structure of the stable homotopy category. We further show how these techniques relate to rigidity questions and how they can be used to study algebraic model
DG CATEGORIES AS EILENBERGMAC LANE SPECTRAL ALGEBRA
, 804
"... Abstract. We construct a zigzag of Quillen equivalences between the homotopy theories of differential graded (=DG) and EilenbergMac Lane spectral (=HR) categories. As an application, every invariant of HRcategories gives rise to an invariant of DG categories. In particular, we obtain a welldefin ..."
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Abstract. We construct a zigzag of Quillen equivalences between the homotopy theories of differential graded (=DG) and EilenbergMac Lane spectral (=HR) categories. As an application, every invariant of HRcategories gives rise to an invariant of DG categories. In particular, we obtain a welldefined topological Hochschild homology theory for DG categories. Moreover, by considering the restriction functor from HRcategories to spectral ones, we obtain a topological equivalence theory, which generalizes previous work by DuggerShipley on DG algebras. In particular, we show that over the rationals Q, two DG categories are topological equivalent if and only
DGALGEBRAS AND DERIVED A∞ALGEBRAS
, 711
"... Abstract. A differential graded algebra can be viewed as an A∞algebra. By a theorem of Kadeishvili, a dga over a field admits a quasiisomorphism from a minimal A∞algebra. We introduce the notion of a derived A∞algebra and show that any dga A over an arbitrary commutative ground ring k is equival ..."
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Abstract. A differential graded algebra can be viewed as an A∞algebra. By a theorem of Kadeishvili, a dga over a field admits a quasiisomorphism from a minimal A∞algebra. We introduce the notion of a derived A∞algebra and show that any dga A over an arbitrary commutative ground ring k is equivalent to a minimal derived A∞algebra. Such a minimal derived A∞algebra model for A is a kprojective resolution of the homology algebra of A together with a family of maps satisfying appropriate relations. As in the case of A∞algebras, it is possible to recover the dga up to quasiisomorphism from a minimal derived A∞algebra model. Hence the structure we are describing provides a complete description of the quasiisomorphism type of the dga. 1.