Tate conjecture

Tate conjecture
John Tate in 1993
FieldAlgebraic geometry and number theory
Conjectured byJohn Tate
Conjectured in1963
Known casesdivisors on abelian varieties
ConsequencesStandard conjectures on algebraic cycles

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 conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture.