Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory

Abstract

We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.

198 pages (thoroughly revised version)

Cited by in corpus (8)

• The character map in (twisted differential) non-abelian cohomology
• Twisted differential cohomology
• Massey products in differential cohomology via stacks
• Differential cohomology theories as sheaves of spectra
• The Beilinson regulator is a map of ring spectra
• The Becker-Gottlieb Transfer Is Functorial
• Noncommutative Differential K-theory
• Local index theory and the Riemann-Roch-Grothendieck theorem for complex flat vector bundles