The categorified Grothendieck–Riemann–Roch theorem

Abstract

In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for Toen and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the Toen-Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.