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

Abstract : 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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Preprints, Working Papers, ...

Cited literature [26 references]

https://hal.archives-ouvertes.fr/hal-00159418
Contributor : Jaya Iyer <>
Submitted on : Tuesday, July 3, 2007 - 11:08:15 PM
Last modification on : Monday, August 19, 2019 - 4:20:06 PM
Long-term archiving on: Tuesday, September 21, 2010 - 1:37:23 PM

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### Identifiers

• HAL Id : hal-00159418, version 2
• ARXIV : 0707.0372

### Citation

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

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