Noether-Lefschetz for \(K_1\) of a certain class of surfaces. (English) Zbl 1059.14012
Let \(Z\) be a general surface in \(\mathbb P^3\) of degree \(d\geq 5\). The aim of the paper under review is to give a new elementary proof of the vanishing of the regulator of \(K_1(Z)\) using a Lefschetz pencil argument. Using similar methods the author also proves the triviality of the regulator for \(K_1\) for the product of two general curves.
Reviewer: Lucian Bădescu (Genova)
MSC:
| 14C35 | Applications of methods of algebraic \(K\)-theory in algebraic geometry |
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 14C25 | Algebraic cycles |
