On the Tate conjecture for the Fano surfaces of cubic threefolds

Abstract

A Fano surface of a smooth cubic threefold X in P^4 parametrizes the lines on X. In this note, we prove that a Fano surface satisfies the Tate conjecture over a field of finite type over the prime field and characteristic not 2.

4 pages ; the first version of this paper has been split into two parts