The categorified Grothendieck-Riemann-Roch theorem

TL;DR

This paper presents a categorification of the Grothendieck-Riemann-Roch theorem, linking advanced algebraic geometry concepts with classical invariants, and establishing new connections between categorified and classical Chern characters.

Contribution

It introduces a categorified version of the Grothendieck-Riemann-Roch theorem and relates it to To"en and Vezzosi's secondary Chern character, bridging modern and classical theories.

Findings

Proves a categorification of the Grothendieck-Riemann-Roch theorem.

Establishes a comparison between categorified and classical Chern characters.

Shows the categorified Chern character recovers the classical de Rham realization.

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 To\"en and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the To\"en-Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.