Field | Algebraic geometry and number theory |
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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.