## Journal of Differential Geometry

### On a conjucture of Kashiwara relating Chern and Euler classes of $\mathcal{O}$-modules

Julien Grivaux

#### 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

http://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. http://projecteuclid.org/euclid.jdg/1335230847.