We propose a categorification of the Chern character that refines earlier work of Toën and Vezzosi and of Ganter and Kapranov. If X is an algebraic stack, our categorified Chern character is a symmetric monoidal functor from a category of mixed noncommutative motives over X , which we introduce, to S1-equivariant perfect complexes on the derived free loop stack LX. As an application of the theory, we show that Toën and Vezzosi's secondary Chern character factors through secondary K -theory. Our techniques depend on a careful investigation of the functoriality of traces in symmetric monoidal (∞,n)-categories, which is of independent interest.\ud\udMSC\ud14F05; 18D05; 19D55
展开▼
机译：我们建议对Chern字符进行分类，以完善Toën和Vezzosi以及Ganter和Kapranov的早期作品。如果X是代数堆栈，则我们分类的Chern字符是对称的单向子函子，它来自X上的混合非交换动机类别，我们将其引入派生自由回路堆栈LX上的S1等价理想复合体。作为该理论的应用，我们通过次要K理论证明了Toën和Vezzosi的次要Chern特征因子。我们的技术取决于对对称单曲面（∞，n）类迹线的功能性的仔细研究，这是与之无关的。\ ud \ udMSC \ ud14F05; 18D05; 19D55
展开▼
