Tate conjecture
John Tate in 1993 | |
| Field | Algebraic geometry and number theory |
|---|---|
| Conjectured by | John Tate |
| Conjectured in | 1963 |
| Known cases | divisors on abelian varieties |
| Consequences | Standard 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.