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

Julien Grivaux (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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.

Mots clés: conjecture of Kashiwara; Grothendieck-Riemann-Roch theorem; Hodge cohomology; Euler class; Chern class; Todd class

Domaines: Géométrie algébrique [math.AG]

Julien Grivaux. On a conjecture of Kashiwara relating Chern and Euler classes of O-modules. Journal of Differential Geometry, 2012, 90 (2), pp.267--275. ⟨hal-01301388⟩