Hodge conjecture


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Hodge conjecture

[′häj kən‚jek·chər]
(mathematics)
The 2 p-dimensional rational cohomology classes in an n-dimensional algebraic manifold M which are carried by algebraic cycles are those with dual cohomology classes representable by differential forms of bidegree (n-p, n-p) on M.
References in periodicals archive ?
Prof Reid added: 'I have had numerous arguments with mathematicians around the world over the Hodge conjecture and it has taken up a large chunk of my life.
Professor Miles Reid, of Warwick University, has spent more than 30 years mulling over the Hodge Conjecture which has baffled academics for decades.
They posted them on the internet and designated a $7million prize for solving the puzzles, $1million for each, including the Hodge Conjecture.
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.