Symmetric monoidal structure on non-commutative motives
Symmetric monoidal structure on non-commutative motives
复制标题
非交换动机上的对称幺半群结构
DOI：
10.1017/is011011005jkt169
复制
发表时间：
2010
影响因子：
--
通讯作者：
Gonçalo Tabuada
中科院分区：
文献类型：
--
作者：
Denis;Gonçalo Tabuada
在本文中，我们进一步研究非交换动机，始于[12,43]。我们的主要成果是在dg类的定域激励子Motlocdg上构造了一个对称单轴结构。作为应用，我们得到：(1)用非连接代数k理论计算了Motlocdg中态射的谱；(2)将Kontsevich的非交换混合动机范畴KMMk完全忠实地嵌入到定位动机的基本范畴Motlocdg(e)中；(3)从非连接代数k -论到负周期循环同调的Chern字符映射的简单构造；(4) Toën次k理论与KMMk的Grothendieck环的精确联系；(5)用Hochschild同调描述KMMk中的欧拉特征。
In this article we further the study of non-commutative motives, initiated in [12, 43]. Our main result is the construction of a symmetric monoidal structure on the localizing motivator Motlocdg of dg categories. As an application, we obtain : (1) a computation of the spectra of morphisms in Motlocdg in terms of non-connective algebraic K-theory; (2) a fully-faithful embedding of Kontsevich's category KMMk of non-commutative mixed motives into the base category Motlocdg(e) of the localizing motivator; (3) a simple construction of the Chern character maps from non-connective algebraic K-theory to negative and periodic cyclic homology; (4) a precise connection between Toën's secondary K-theory and the Grothendieck ring of KMMk; (5) a description of the Euler characteristic in KMMk in terms of Hochschild homology.