Higher traces, noncommutative motives, and the categorified Chern character
By Marc Hoyois, Sarah Scherotzke, Nicolò Sibilla. 2015
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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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5f6c84656b9bee2b68486ca35bfd6003170e3c6d
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, background): “g [12, 84, 38, 48], but here we only recall the relevant details in the case of Hochschild homology of categories.”