Higher traces, noncommutative motives, and the categorified Chern character

DOI10.1016/j.aim.2017.01.008zbMath1361.14014arXiv1511.03589OpenAlexW2964290142MaRDI QIDQ509666

Marc Hoyois, Sarah Scherotzke, Nicolò Sibilla

Publication date: 17 February 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.03589

zbMATH Keywords

tracesnoncommutative motivesChern characterssecondary \(K\)-theory

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55)

Related Items

The integral Hodge conjecture for two-dimensional Calabi–Yau categories ⋮ Descent in algebraic \(K\)-theory and a conjecture of Ausoni-Rognes ⋮ Gluing semi-orthogonal decompositions ⋮ The fundamental theorem of localizing invariants ⋮ Wrapped sheaves ⋮ Additivity of the motivic trace and the motivic Euler-characteristic ⋮ Coherent Springer theory and the categorical Deligne-Langlands correspondence ⋮ An equivalence between enriched \(\infty \)-categories and \(\infty \)-categories with weak action ⋮ Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes ⋮ Real representation theory of finite categorical groups ⋮ Kaledin's degeneration theorem and topological Hochschild homology ⋮ Descent for semiorthogonal decompositions ⋮ (Op)lax natural transformations, twisted quantum field theories, and ``even higher Morita categories ⋮ Derived Azumaya algebras and twisted \(K\)-theory ⋮ The categorified Grothendieck–Riemann–Roch theorem ⋮ Relative Calabi-Yau structures. II: Shifted Lagrangians in the moduli of objects ⋮ Hyperdescent and étale \(K\)-theory ⋮ Twisted iterated algebraic \(K\)-theory and topological T-duality for sphere bundles ⋮ A toy model for the Drinfeld-Lafforgue shtuka construction ⋮ On the \(K\)-theory of pullbacks ⋮ Categorical traces and a relative Lefschetz–Verdier formula

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localization theorems in topological Hochschild homology and topological cyclic homology
• \(K\)-theory and the bridge from motives to noncommutative motives
• (Op)lax natural transformations, twisted quantum field theories, and ``even higher Morita categories
• Day convolution for \(\infty\)-categories
• \(\mathbf{A}^1\)-homotopy theory of noncommutative motives
• Higher \(K\)-theory via universal invariants
• On the algebraic \(K\)-theory of the complex \(K\)-theory spectrum
• \(\mathbb{A}^1\)-homotopy theory
• On the cyclic homology of ringed spaces and schemes
• Algebraic \(K\)-theory of topological \(K\)-theory
• A universal characterization of higher algebraic \(K\)-theory
• Chern characters, equivariant traces and derived algebraic geometry
• Brauer groups and étale cohomology in derived algebraic geometry
• Uniqueness of the multiplicative cyclotomic trace
• Representation and character theory in 2-categories
• A note on secondary \(K\)-theory
• On the algebraicK-theory of higher categories
• Symmetric monoidal structure on non-commutative motives
• Lectures on DG-Categories
• Algèbres simplicialesS¹-équivariantes, théorie de de Rham et théorèmes HKR multiplicatifs
• Integral transforms and Drinfeld centers in derived algebraic geometry
• Sheaves of categories and the notion of 1-affineness
• On the Classification of Topological Field Theories
• Chern Character, Loop Spaces and Derived Algebraic Geometry
• Higher Topos Theory (AM-170)
• The additivity of traces in triangulated categories