The categorified Grothendieck-Riemann-Roch theorem

Hoyois, Marc; Safronov, Pavel; Scherotzke, Sarah; Sibilla, Nicolò

doi:10.1112/S0010437X20007642

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The categorified Grothendieck-Riemann-Roch theorem

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Sibilla, Nicolò
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/S0010437X20007642
(Publisher version)

https://doi.org/10.48550/arXiv.1804.00879
(Preprint)

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Citation

Hoyois, M., Safronov, P., Scherotzke, S., & Sibilla, N. (2021). The categorified Grothendieck-Riemann-Roch theorem. Compositio Mathematica, 157(1), 154-214. doi:10.1112/S0010437X20007642.

Cite as: https://hdl.handle.net/21.11116/0000-0008-66AA-6

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.