| Résume | This is joint work with Jaya Iyer. We recall that to a flat bundle one can associate the regulator or secondary Chern class invariants in $H^{2p−1}(X, \mathbb{C}\backslash\mathbb{Z})$. Reznikov showed that if $X$ is a smooth projective variety then these invariants are torsion. Following suggestions of Deligne, given a flat bundle over a quasiprojective variety $X=\overline{X}\backslash D$ with unipotent monodromy around the snc divisor $D$, we define secondary Chern classes in $H^{2p−1}(X, \mathbb{C}\backslash\mathbb{Z})$ using patched connections whose curvature forms are nilpotent. We follow Reznikov’s strategy to show that these invariants are torsion, using Mochizuki’s theorem on deformation to a VHS. This requires defining the extended patched classes in K-theory. It follows that the Deligne Chern classes of the Deligne canonical extended bundle on $X$ are torsion |
