Burgos Gil, José I.Wang, Steve2020-03-052020-03-051996https://hdl.handle.net/2445/152118Preprint enviat per a la seva publicació en una revista científica: Inventiones mathematicae, 1998, vol. 132, pp. 261–305. [https://doi.org/10.1007/s002220050224]In this paper, we prove a Gauss-Bonnet theorem for the higher algebraic K-theory of smooth complex algebraic varieties. To each exact n-cube of hermitian vector bundles, we associate a higher Bott-Chen form, generalizing the Bott-Chern forms associated to exact sequences. These forms allow us to define characteristic classes from K-theory to absolute Hodge cohomology. Then we prove that these characteristic classes agree with Beilinson's regulator map.37 p.application/pdfeng(c) José Ignacio Burgos et al., 1996K-teoriaVarietats algebraiquesUniversitat de Barcelona. Institut de Matemàticainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess