The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques

Abstract

In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.

21 pages. Comments are welcome. Final version. To appear in Journal of Geometry and Physics

References in corpus (5)

• An index theorem in differential K-theory
• Differential K-theory. A survey
• Structured vector bundles define differential K-theory
• Arakelov motivic cohomology I
• Functoriality of equivariant eta forms