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.
The categorified Grothendieck-Riemann-Roch theorem / Hoyois, M.; Safronov, P.; Scherotzke, S.; Sibilla, N.. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 157:1(2021), pp. 154-214. [10.1112/S0010437X20007642]
The categorified Grothendieck-Riemann-Roch theorem
Sibilla, N.
2021-01-01
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 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.| File | Dimensione | Formato | |
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