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 ?

The Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety.

Rational coefficients

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.

The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time

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.

But Prof Reid, 52, claims the Hodge Conjecture will never be solved and has instead channelled his efforts into disproving the complex algebraic theory.