Adelic Chern forms and applications

Reinhold Hübl, Amnon Yekutieli

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Let X be a variety over a field of characteristic 0. Given a vector bundle E on X we construct Chern forms ci(E; ∇) ∈ Γ(X, A2iX). Here ȦX is the sheaf of Beilinson adeles and ∇ is an adelic connection. When X is smooth HPΓ(X, ȦX) = HPDR(X), the algebraic De Rham cohomology, and Ci(E) = [ci(E; ∇)] 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.

Original languageEnglish
Pages (from-to)797-839
Number of pages43
JournalAmerican Journal of Mathematics
Issue number4
StatePublished - 1 Jan 1999

ASJC Scopus subject areas

  • Mathematics (all)


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