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. Helge Holden Ragni Piene The Abel Prize 2008-2012 http://books.google.com/books?id=VrG9BAAAQBAJ&pg=PA299 21 January 2014 Springer Science & Business Media 978-3-642-39449-2 299 External links Category:Conjectures Category:Number theory