Chern classes in Deligne cohomology for coherent analytic sheaves

Julien Grivaux (1)

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

In this article, we construct Chern classes in rational Deligne cohomology for coherent sheaves on a smooth complex compact manifold. We prove that these classes satisfy the functorial-ity property under pullbacks, the Whitney formula and the Grothendieck-Riemann-Roch theorem for projective morphisms between smooth complex compact manifolds.

Domaines: Géométrie algébrique [math.AG]

Julien Grivaux. Chern classes in Deligne cohomology for coherent analytic sheaves. Mathematische Annalen, 2010, 347, pp.249 - 284. ⟨10.1007/s00208-009-0430-9⟩. ⟨hal-01397887⟩