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Millenium Problems


Geometry » Algebraic Geometry

The Hodge Conjecture ★★★★

Author(s): Hodge

Conjecture   Let $ X $ be a complex projective variety. Then every Hodge class is a rational linear combination of the cohomology classes of complex subvarieties of $ X $.

Keywords: Hodge Theory; Millenium Problems

Posted by Charles
updated July 13th, 2008
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Theoretical Comp. Sci. » Algorithms

P vs. NP ★★★★

Author(s): Cook; Levin

Problem   Is P = NP?

Keywords: Complexity Class; Computational Complexity; Millenium Problems; NP; P; polynomial algorithm

Posted by zitterbewegung
updated October 18th, 2007
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Number Theory » Analytic N.T.

The Riemann Hypothesis ★★★★

Author(s): Riemann

The zeroes of the Riemann zeta function that are inside the Critical Strip (i.e. the vertical strip of the complex plane where the real part of the complex variable is in ]0;1[), are actually located on the Critical line ( the vertical line of the complex plane with real part equal to 1/2)

Keywords: Millenium Problems; zeta

Posted by eric
updated January 27th, 2013
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