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The categorified Grothendieck–Riemann–Roch theorem


Hoyois, Marc; Safronov, Pavel; Scherotzke, Sarah; Sibilla, Nicolò (2021). The categorified Grothendieck–Riemann–Roch theorem. Compositio Mathematica, 157(1):154-214.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Uncontrolled Keywords:Algebra and Number Theory
Language:English
Date:1 January 2021
Deposited On:02 Dec 2021 11:59
Last Modified:26 Apr 2024 01:36
Publisher:Cambridge University Press
ISSN:0010-437X
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1112/s0010437x20007642