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Blaise Pascal
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Abhishek Banerjee
Les motifs de Tate et les opérateurs de périodicité de Connes
(Tate motives and the periodicity operators of Connes)
Annales mathématiques Blaise Pascal, 21 no. 1 (2014), p. 1-23, doi: 10.5802/ambp.333
Article PDF | Reviews MR 3248219 | Zbl 06329054
Class. Math.: 14F42
Keywords: Tate motives, periodicity operators

Résumé - Abstract

In this paper, we define a category $\widetilde{Mot}_{\mathbf{C}}$ of motives over a symmetric monoidal category $(\mathbf{C},\otimes ,1)$ satisfying certain conditions. The role of spaces over $(\mathbf{C},\otimes ,1)$ is played by monoid objects (not necessarily commutative) in $\mathbf{C}$. To define morphisms in the category $\widetilde{Mot}_{\mathbf{C}}$, we use classes in bivariant cyclic homology groups. The aim is to show that the Connes periodicity operators induce morphisms $M\otimes \mathbb{T}^{\otimes 2} \longrightarrow M$ in $\widetilde{Mot}_{\mathbf{C}}$, where $\mathbb{T}$ is the Tate motive in $\widetilde{Mot}_{\mathbf{C}}$.

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