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arXiv · 1511.03589

Higher traces, noncommutative motives, and the categorified Chern character

Marc Hoyois·Sarah Scherotzke·Nicolò Sibilla
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Abstract

We propose a categorification of the Chern character that refines earlier work of To\"en 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 To\"en 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 (infinity,n)-categories, which is of independent interest.

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Marc Hoyois, Sarah Scherotzke, Nicolò Sibilla. 2015-11-11. Higher traces, noncommutative motives, and the categorified Chern character. https://arxiv.org/abs/1511.03589

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