Arkiv för Matematik

Volume 61 (2023)

Number 1

Intersection theory and Chern classes in Bott–Chern cohomology

Pages: 211 – 265



Xiaojun Wu (Mathematics VIII, Universität Bayreuth, Germany)


In this article, we study the axiomatic approach of Grivaux in [Gri10] for rational Bott–Chern cohomology, and use it in particular to define Chern classes of coherent sheaves in rational Bott–Chern cohomology. This method also allows us to derive a Riemann–Roch–Grothendieck formula for a projective morphism between smooth complex compact manifolds.

Received 16 June 2021

Received revised 29 September 2022

Accepted 10 October 2022

Published 26 April 2023