Regulators of canonical extensions are torsion: the smooth divisor case

Jaya Iyer (1, 2) , Carlos Simpson (3)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 School of Mathematics [Princeton]
3 JAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Géométrie algébrique [math.AG]

Jaya Iyer, Carlos Simpson. Regulators of canonical extensions are torsion: the smooth divisor case. 2007. ⟨hal-00159418v2⟩