The Noether–Lefschetz theorem in arbitrary characteristic

Abstract: 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).

algebraic geometry

Audience: researchers in the topic

Algebraic Geometry NorthEastern Series (AGNES)