Regulators of canonical extensions are torsion: the smooth divisor case

Details Regulators of canonical extensions are torsion: the smooth divisor case Regulators of canonical extensions are torsion: the smooth divisor case

2007-07-03

arxiv.org/abs/0707.0372v2

Mathematics

Algebraic Geometry

Scientific paper

In this paper, we prove a generalization of Reznikov's theorem which says that the Chern-Simons classes and in particular the Deligne Chern classes (in degrees $>1$) are torsion, of a flat bundle on a smooth complex projective variety. We consider the case of a smooth quasi--projective variety with an irreducible smooth divisor at infinity. We define the Chern-Simons classes of Deligne's canonical extension of a flat vector bundle with unipotent monodromy at infinity, which lift the Deligne Chern classes and prove that these classes are torsion.

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