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.
  • Helge Holden; Ragni Piene (21 January 2014). The Abel Prize 2008-2012. Springer Science & Business Media. p. 299. ISBN 978-3-642-39449-2. 

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