Titre On singular Bott Chern forms.

Résumé :

The singular Bott-Chern forms measure the failure of an exact Riemann-Roch theorem at the level of currents. They are the key ingredient in the definition of direct images of hermitian vector bundles under closed immersions and in the proof of the arithmetic Riemann-Roch theorem in Arakelov geometry for closed immersions. There are two definitions of singular Bott-Chern forms. The first due to Bismut, Gillet and Soulé uses the formalism of super connections. The second, due to Zha, is an adaptation of the original definition of Bott-Chern classes by Bott and Chern. In this talk we wil give an axiomatic characterization of singular Bott-Chern, which is similar to the characterization of Bott-Chern forms, but that depends on the choice of an arbitrary characteristic class. This characterization allows us to give a new definition of singular Bott-Chern forms by means of the deformation to the normal cone technique and to compare the previous definitions of singular Bott-Chern forms.

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