Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778716 | Advances in Mathematics | 2017 | 58 Pages |
Abstract
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 (â,n)-categories, which is of independent interest.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marc Hoyois, Sarah Scherotzke, Nicolò Sibilla,