  Using the theory of mixed perverse sheaves, we extend arguments on the Hodge
conjecture initiated by Lefschetz and Griffiths to the case of the Tate
conjecture, and show that the Tate conjecture for divisors is closely related
to the de Rham conjecture for nonproper varieties, finiteness of the
Tate-Shafarevich groups, and also to some conjectures in the analytic number
theory.
