Tate conjecture

In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The Tate conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture.

Quotes

 * The twin conjectures of Hodge and Tate have a status in algebraic and arithmetic geometry similar to that of the Riemann hypothesis in analytic number theory.