Journal
COMPOSITIO MATHEMATICA
Volume 157, Issue 1, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1112/S0010437X20007642
Keywords
Chern character; K-theory; categorification
Categories
Funding
- NCCR SwissMAP grant of the Swiss National Science Foundation
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The paper proves a categorification of the Grothendieck-Riemann-Roch theorem, establishing a connection with Toen and Vezzosi's secondary Chern character. It compares the Toen-Vezzosi Chern character with the classical Chern character, demonstrating that the categorified Chern character can recover the classical de Rham realization.
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.
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