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Teleman C., Openclosed field theories, string topology, and Hochschild homology
 in Alpine Perspectives on Algebraic Topology, Editors
"... and Hochschild homology ..."
A guided tour through the garden of noncommutative motives. Available at arXiv:1108.3787
"... Abstract. These are the extended notes of a survey talk on noncommutative motives given at the 3 era Escuela de Inverno Luis SantalóCIMPA Research ..."
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Abstract. These are the extended notes of a survey talk on noncommutative motives given at the 3 era Escuela de Inverno Luis SantalóCIMPA Research
TORSION INVARIANTS FOR TRIANGULATED CATEGORIES
"... The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasiisomorphisms. Such examples are called ‘algebraic ’ because they have underlying abelian (or at least additive) categories. Stable homotopy theory ..."
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The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasiisomorphisms. Such examples are called ‘algebraic ’ because they have underlying abelian (or at least additive) categories. Stable homotopy theory produces examples of triangulated categories by quite different means, and in this context the underlying categories are usually very ‘nonadditive ’ before passing to homotopy classes of morphisms. We call such triangulated categories topological, compare Definition 3.1; this class includes the algebraic triangulated categories. The purpose of this paper is to explain some systematic differences between these two kinds of triangulated categories. There are certain properties – defined entirely in terms of the triangulated structure – which hold in all algebraic examples, but which can fail in general. These differences are all torsion phenomena, and rationally every topological triangulated category is algebraic (at least under mild size restrictions). Our main tool is a new numerical invariant, the norder of an object in a triangulated category, for n a natural number (see Definition 1.1). The norder is a nonnegative integer (or infinity), and an object Y has positive norder if and only if n · Y = 0; the norder can be thought of
Contents
, 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,
Contents
, 902
"... Abstract. In this paper, we further the study of spectral categories, initiated in [26]. Our main contribution is the construction of the Universal matrix invariant of spectral categories, i.e. a functor U with values in an additive category, which inverts the Morita equivalences, satisfies matrix i ..."
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Abstract. In this paper, we further the study of spectral categories, initiated in [26]. Our main contribution is the construction of the Universal matrix invariant of spectral categories, i.e. a functor U with values in an additive category, which inverts the Morita equivalences, satisfies matrix invariance, and is universal with respect to these two properties. For example, the algebraic Ktheory and the topological Hochschild and cyclic homologies are matrix invariants, and so they factor uniquely through U. As an application, we obtain for free nontrivial trace maps from the Grothendieck group to the topological
ON THE NEGATIVE KTHEORY OF SCHEMES IN FINITE CHARACTERISTIC
, 811
"... Abstract. We show that if X is a ddimensional scheme of finite type over a perfect field k of characteristic p> 0, then Ki(X) = 0 and X is Kiregular for i < −d −2 whenever the resolution of singularities holds over k. This proves the Kdimension conjecture of Weibel [22, 2.9] (except for −d − 1 ≤ ..."
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Abstract. We show that if X is a ddimensional scheme of finite type over a perfect field k of characteristic p> 0, then Ki(X) = 0 and X is Kiregular for i < −d −2 whenever the resolution of singularities holds over k. This proves the Kdimension conjecture of Weibel [22, 2.9] (except for −d − 1 ≤ i ≤ −d − 2) in all characteristics, assuming the resolution of singularities. 1.
Contents
, 902
"... Abstract. In this paper we pursue the study of spectral categories initiated in [19]. More precisely, we construct the Universal Additive Invariant of spectral categories, i.e. a functorUa with values in an additive category Add, which inverts the Morita equivalences, satisfies additivity, and is un ..."
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Abstract. In this paper we pursue the study of spectral categories initiated in [19]. More precisely, we construct the Universal Additive Invariant of spectral categories, i.e. a functorUa with values in an additive category Add, which inverts the Morita equivalences, satisfies additivity, and is universal with respect to these properties. For example, the algebraic Ktheory, the topological Hochschild homology, the topological cyclic homology,... are all additive invariants, and so they factor uniquely throw Ua. As an application of our construction, we obtain for free nontrivial trace maps from the Grothendieck
MULTIPLICATIVE PROPERTIES OF QUINN SPECTRA
, 907
"... Abstract. We give a simple sufficient condition for Quinn’s “bordismtype spectra ” to be weakly equivalent to strictly associative ring spectra. We also show that Poincaré bordism and symmetric Ltheory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements invo ..."
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Abstract. We give a simple sufficient condition for Quinn’s “bordismtype spectra ” to be weakly equivalent to strictly associative ring spectra. We also show that Poincaré bordism and symmetric Ltheory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn’s functor from bordismtype theories to spectra lifts to the category of symmetric spectra. We also give a new account of the foundations.