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Higher traces, noncommutative motives, and the categorified Chern character

Hoyois, Marc, Scherotzke, Sarah, Sibilla, Nicolo (2017) Higher traces, noncommutative motives, and the categorified Chern character. Advances in Mathematics, 309 . pp. 97-154. ISSN 0001-8708. E-ISSN 1090-2082. (doi:10.1016/j.aim.2017.01.008) (KAR id:60899)

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https://doi.org/10.1016/j.aim.2017.01.008

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 (?,n)-categories, which is of independent interest.

MSC

14F05; 18D05; 19D55

Item Type: Article
DOI/Identification number: 10.1016/j.aim.2017.01.008
Uncontrolled keywords: Traces; Noncommutative motives; Chern characters; Secondary K-theory
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Nicolo Sibilla
Date Deposited: 14 Mar 2017 10:01 UTC
Last Modified: 06 May 2020 03:15 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60899 (The current URI for this page, for reference purposes)
Sibilla, Nicolo: https://orcid.org/0000-0003-4438-7369
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