The classical Noether-Lefschetz theorem says that for a very general surface S of degree 4 in P^3 over the complex numbers, the restriction map from the divisor class group on P^3 to S is an isomorphism. In this talk, we will show a Noether-Lefschetz result for varieties over fields of arbitrary characteristic. The proof uses the relative Jacobian of a curve fibration, and it also works for singular varieties (for Weil divisors). We will not use any Hodge theory, cohomology, or monodromy. Speaker(s): Lena Ji (University of Michigan)