An infinitesimal Noether–Lefschetz theorem for Chow groups

Abstract

Let X be a smooth, complex projective variety, and Y be a very general, sufficiently ample hypersurface in X. A conjecture of M.V. Nori states that the natural restriction map CHp(X)Q→CHp(Y)Q is an isomorphism for all p<dim⁡Y and an injection for p=dim⁡Y. This is the generalized Noether–Lefschetz conjecture. We prove an infinitesimal version of this conjecture.