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Chern classes in Deligne cohomology for coherent analytic sheaves

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



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