In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for Toën and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the Toën-Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.
|Publication status||Published - 15 Feb 2021|
- 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
- 19D55 K-theory and homology; cyclic homology and cohomology