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

Abstract

We develop differential algebraic K-theory of regular arithmetic schemes. Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using differential forms. We construct a cycle map which represents differential algebraic K-theory classes by geometric vector bundles. As an application we derive Lott's relation between short exact sequences of geometric bundles with a higher analytic torsion form.

106 pages (corrects a mistake in the sheaf condition), published version

References in corpus (9)

• Higher Topos Theory
• An index theorem in differential K-theory
• Structured vector bundles define differential K-theory
• Arakelov motivic cohomology I
• Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory
• Hodge filtered complex bordism
• Differential cohomology theories as sheaves of spectra
• Differential cohomology
• Another viewpoint on J-spaces

Cited by in corpus (8)

• Mixed Hodge structures and formality of symmetric monoidal functors
• The Beilinson regulator is a map of ring spectra
• Multiplicative differential algebraic K-theory and applications
• Differential cohomology (encyclopedia article)
• Homotopy theory of smooth compactifications of algebraic varieties
• An approximation of the $e$-invariant in the stable homotopy category
• A stable splitting of factorisation homology of generalised surfaces
• $\mathrm{G}$-theory of ${\mathbb{F}}_1$-algebras I: the equivariant Nishida problem