Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves
arXiv:0809.2815
Abstract
We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations X over curves over perfect fields k. For example, if k is finitely generated over Q and the fibration has odd relative dimension at least 11, then CH^{i}(X) is finitely generated for i<=4.
13 pages