Adelic Chern Forms and Applications

Reinhold Huebl; Amnon Yekutieli

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arXiv · math/9811109

Adelic Chern Forms and Applications

Reinhold Huebl·Amnon Yekutieli

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Abstract

Let X be a variety over a field of characteristic 0. Given a vector bundle E on X we construct Chern forms c_{i}(E;\nabla) in Γ(X, \cal{A}^{2i}_{X}). Here \cal{A}^{.}_{X} is the sheaf Beilinson adeles and \nabla is an adelic connection. When X is smooth these adeles calculate the algebraic De Rham cohomology, and c_{i}(E) = [c_{i}(E;\nabla)] are the usual Chern classes. We include three applications of the construction: (1) existence of adelic secondary (Chern-Simons) characteristic classes on any smooth X and any vector bundle E; (2) proof of the Bott Residue Formula for a vector field action; and (3) proof of a Gauss-Bonnet Formula on the level of differential forms, namely in the De Rham-residue complex.

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BibTeX RIS

Reinhold Huebl, Amnon Yekutieli. 1998-11-18. Adelic Chern Forms and Applications. https://arxiv.org/abs/math/9811109

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