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Homotopy theory of comodules over a Hopf algebroid
, 2003
"... Given a good homology theory E and a topological space X, E∗X is not just an E∗module but also a comodule over the Hopf algebroid (E∗, E∗E). We establish a framework for studying the homological algebra of comodules over a wellbehaved Hopf algebroid (A, Γ). That is, we construct ..."
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Cited by 27 (3 self)
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Given a good homology theory E and a topological space X, E∗X is not just an E∗module but also a comodule over the Hopf algebroid (E∗, E∗E). We establish a framework for studying the homological algebra of comodules over a wellbehaved Hopf algebroid (A, Γ). That is, we construct
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, 2005
"... Abstract. Let A be an algebra over an operad in a cocomplete closed symmetric ..."
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Abstract. Let A be an algebra over an operad in a cocomplete closed symmetric
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, 903
"... Abstract. In this article, we further the study of higher Ktheory of dg categories via universal invariants, initiated in [33]. Our main result is the corepresentability of nonconnective Ktheory by the base ring in the universal localizing motivator. As an application, we obtain for free higher C ..."
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Abstract. In this article, we further the study of higher Ktheory of dg categories via universal invariants, initiated in [33]. Our main result is the corepresentability of nonconnective Ktheory by the base ring in the universal localizing motivator. As an application, we obtain for free higher Chern characters, resp. higher trace maps, from negative Ktheory to cyclic homology,
Fakultät für Mathematik
, 2014
"... The purpose of this work is to give a definition of a topological Ktheory for dgcategories over C and to prove that the Chern character map from algebraic Ktheory to periodic cyclic homology descends naturally to this new invariant. This topological Chern map provides a natural candidate for the ..."
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The purpose of this work is to give a definition of a topological Ktheory for dgcategories over C and to prove that the Chern character map from algebraic Ktheory to periodic cyclic homology descends naturally to this new invariant. This topological Chern map provides a natural candidate for the existence of a rational structure on the periodic cylic homology of a smooth proper dgalgebra, within the theory of noncommutative Hodge structures. The definition of topological Ktheory consists in two steps: taking the topological realization of algebraic Ktheory, and inverting the Bott element. The topological realization is the left Kan extension of the functor ”space of complex points ” to all simplicial presheaves over complex algebraic varieties. Our first main result states that the topological Ktheory of the unit dgcategory is the spectrum BU. For this we are led to prove a homotopical generalization of Deligne’s cohomological proper descent, using Lurie’s proper descent. The fact that the Chern character descends to topological Ktheory is established by using Kassel’s Künneth formula for periodic cyclic homology and once again the proper descent result. In the case of a dgcategory of perfect complexes on a smooth scheme, we show that we recover the usual topological K