Regulators and cycle maps in higher-dimensional differential algebraic \(K\)-theory

DOI10.1016/j.aim.2015.08.004zbMath1333.19007arXiv1311.1421OpenAlexW1863543717MaRDI QIDQ887351

Ulrich Bunke, Georg Tamme

Publication date: 28 October 2015

Published in: Advances in Mathematics, Annals of \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.1421

zbMATH Keywords

dilogarithmregulatorregulatorsdifferential cohomologyDeligne cohomologyabsolute Hodge cohomologyBeilinson's regulatordifferential algebraic \(K\)-theoryLott's conjectureSteinberg relation

Mathematics Subject Classification ID

Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Higher logarithm functions (33B30) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Twisted (K)-theory; differential (K)-theory (19L50)

Related Items (5)

The Beilinson regulator is a map of ring spectra ⋮ A regulator for smooth manifolds and an index theorem ⋮ \(G \)-theory of \(\mathbb F_1\)-algebras I: the equivariant Nishida problem ⋮ Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic 𝐾-theory ⋮ Chern-Simons invariants in \textit{KK}-theory

Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Landweber exact formal group laws and smooth cohomology theories
• Characteristic classes for algebraic vector bundles with Hermitian metric. II
• Characteristic classes for algebraic vector bundles with Hermitian metric. I
• Théorie générale des classes caractéristiques secondaires. (General theory of secondary characteristic classes)
• An index theorem in differential \(K\)-theory
• Higher Bott-Chern forms and Beilinson's regulator
• Imbedding of an abstract variety in a complete variety
• The transfer map and fiber bundles
• Analytic torsion and R-torsion of Riemannian manifolds
• Analytic torsion and the heat equation
• Homotopy invariant algebraic structures on topological spaces
• Quasi-categories and Kan complexes
• A parametrized index theorem for the algebraic \(K\)-theory Euler class.
• Quadratic functions in geometry, topology, and \(M\)-theory
• Théorie de Hodge. II. (Hodge theory. II)
• Théorie de Hodge. III
• Higher arithmetic \(K\)-theory
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• The Regulators of Beilinson and Borel
• Arakelov motivic cohomology II
• Uniqueness of smooth extensions of generalized cohomology theories
• Smooth K-Theory
• Index theory, eta forms, and Deligne cohomology
• Higher algebraic K-theory: I
• Stable real cohomology of arithmetic groups
• Secondary analytic indices
• Flat Vector Bundles, Direct Images and Higher Real Analytic Torsion
• Hodge filtered complex bordism
• Axiomatic characterization of ordinary differential cohomology
• Higher Topos Theory (AM-170)
• On Ramond-Ramond fields and \(K\)-theory

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