The categorified Grothendieck-Riemann-Roch theorem

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.

Automated summary

The paper proves a categorification of the Grothendieck-Riemann-Roch theorem, establishing a connection with Toen and Vezzosi's secondary Chern character. It compares the Toen-Vezzosi Chern character with the classical Chern character, demonstrating that the categorified Chern character can recover the classical de Rham realization.