On a conjecture of Kashiwara relating Chern and Euler classes of O-modules

Abstract

In this note we prove a conjecture of Kashiwara, which states that the Euler class of a coherent analytic sheaf F on a complex manifold X is the product of the Chern character of 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.

Final version

References in corpus (2)

• Deformation quantization modules
• The relative Riemann-Roch theorem from Hochschild homology

Cited by in corpus (3)

• Microlocal Euler classes and Hochschild homology
• Derived geometry of the first formal neighborhood of a smooth analytic cycle
• A variant of the Mukai pairing via deformation quantization