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In this note, we report on a work jointly done with C. Simpson on ageneralization of Reznikov's theorem which says that the Chern-Simons classesand in particular the Deligne Chern classes (in degrees $> 1$) are torsion, ofa flat vector bundle on a smooth complex projective variety. We consider thecase of a smooth quasi--projective variety with an irreducible smooth divisorat infinity. We define the Chern-Simons classes of the Deligne's\textit{canonical extension} of a flat vector bundle with unipotent monodromyat infinity, which lift the Deligne Chern classes and prove that these classesare torsion. The details of the proof can be found in arxiv:0707.0372[math.AG].

A report on "Regulators of canonical extension are torsion; the smooth divisor case"