Journal of Differential Geometry
- J. Differential Geom.
- Volume 90, Number 2 (2012), 267-275.
On a conjucture of Kashiwara relating Chern and Euler classes of $\mathcal{O}$-modules
Abstract
In this note we prove a conjecture of Kashiwara, which states that the Euler class of a coherent analytic sheaf $\mathcal{F}$ on a complex manifold $X$ is the product of the Chern character of $\mathcal{F}$ with the Todd class of $X$. As a corollary, we obtain a functorial proof of the Grothendieck–Riemann–Roch theorem in Hodge cohomology for complex manifolds.
Article information
Source
J. Differential Geom., Volume 90, Number 2 (2012), 267-275.
Dates
First available in Project Euclid: 24 April 2012
Permanent link to this document
https://projecteuclid.org/euclid.jdg/1335230847
Digital Object Identifier
doi:10.4310/jdg/1335230847
Mathematical Reviews number (MathSciNet)
MR2899876
Zentralblatt MATH identifier
1247.32013
Citation
Grivaux, Julien. On a conjucture of Kashiwara relating Chern and Euler classes of $\mathcal{O}$-modules. J. Differential Geom. 90 (2012), no. 2, 267--275. doi:10.4310/jdg/1335230847. https://projecteuclid.org/euclid.jdg/1335230847
