{"paper":{"title":"Higher traces, noncommutative motives, and the categorified Chern character","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.CT","math.RT"],"primary_cat":"math.KT","authors_text":"Marc Hoyois, Nicol\\`o Sibilla, Sarah Scherotzke","submitted_at":"2015-11-11T17:51:29Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03589","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}