This is a substantial revision of the older version of this paper. The main result of the old version (the equality, up to a factor of 2 of the Beilinson and Borel regulators) is now a conjecture. The main results give equality of Beilinson chern classes and Cheeger-Simons-Chern classes in various situations such as for flat bundles over quasi projective varieties. We also prove the equality (up to a factor of two) of the Borel regulator element and the universal Cheeger-Simons Chern class.
Categories: alg-geom math.AG