Abstract.
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.
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Oblatum 21-III-1997 & 12-VI-1997
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Burgos, J., Wang, S. Higher Bott-Chern forms and Beilinson's regulator. Invent math 132, 261–305 (1998). https://doi.org/10.1007/s002220050224
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DOI: https://doi.org/10.1007/s002220050224