Regulators and cycle maps in higher-dimensional differential algebraic   K-theory
  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. 
Ulrich Bunke and Georg Tamme
math.NT math.AG math.KT