The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields

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 L-functions. We prove the conjecture for certain classes of non-isotrivial varieties over Fq(t), including some cubic threefolds and fivefolds. 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.