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.

中文翻译：

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分类的Grothendieck–Riemann–Roch定理

在本文中，我们证明了Grothendieck–Riemann–Roch定理的分类。我们的结果特别暗示了Toën和Vezzosi的次要Chern角色的Grothendieck–Riemann–Roch定理。作为主要应用，我们建立了Toën–Vezzosi Chern角色与经典Chern角色之间的比较，并表明分类的Chern角色恢复了de Rham的经典实现。