Arithmetic and Geometry of a Generic Hypersurface Section

摘要

If the Hodge conjecture (respectively the Tate conjecture or the Mumford - Tateconjecture) holds for a smooth projective variety X over a field k of characteristic zero, then it holds for a generic member X(sub t) of a k-rational Lefschetz pencil of hypersurface sections of X of sufficiently high degree. The