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Hodge conjecture

   Also found in: Wikipedia 0.01 sec.
Hodge conjecture [′häj kən‚jek·chər]
(mathematics)
The 2p-dimensional rational cohomology classes in ann-dimensional algebraic manifoldMwhich are carried by algebraic cycles are those with dual cohomology classes representable by differential forms of bidegree (n-p, n-p) onM.


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Specifically, they are the Riemann hypothesis, which lingers from Hilbert's list, Yang-Mills theory and the mass gap hypothesis, the P Versus NP problem, the Navier-Stokes equations, the Poincaire conjecture, the Birch and Swinnerton-Dyer conjecture, and the Hodge conjecture.
Professor Miles Reid, of Warwick University, has spent more than 30 years mulling over the Hodge Conjecture which has baffled academics for decades.
 
 
 
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