Paper
The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields
Authors
Matt Broe
Abstract
The Beilinson-Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of -functions. We prove the conjecture for certain classes of non-isotrivial varieties over , including some cubic threefolds. We deduce the Birch and Swinnerton-Dyer conjecture for their intermediate Jacobians, and use it to establish new cases of the Tate conjecture over finite fields. We also prove some additional results on the arithmetic of these intermediate Jacobians.