The categorified Grothendieck-Riemann-Roch theorem

Marc Hoyois; Pavel Safronov; Sarah  Scherotzke; Nicolò  Sibilla

doi:10.1112/S0010437X20007642

The categorified Grothendieck-Riemann-Roch theorem

Marc Hoyois, Pavel Safronov, Sarah Scherotzke, Nicolò Sibilla

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Pages (from-to)	154-214
Journal	Compositio Mathematica
Volume	157
Issue number	1
DOIs	https://doi.org/10.1112/S0010437X20007642
Publication status	Published - 15 Feb 2021

Keywords

14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
19D55 K-theory and homology; cyclic homology and cohomology

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10.1112/S0010437X20007642

1804.00879(3)Accepted author manuscript, 799 KB

https://arxiv.org/abs/1804.00879

Cite this

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AB - 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.

KW - 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry

KW - 19D55 K-theory and homology; cyclic homology and cohomology

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The categorified Grothendieck-Riemann-Roch theorem

Abstract

Keywords

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