High Quality Content by WIKIPEDIA articles! The Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de Rham cohomology classes are algebraic, that is, they are sums of Poincare duals of the homology classes of subvarieties. The Hodge conjecture is one of the Clay Mathematics Institute's Millennium Prize Problems, with a prize of $1,000,000 for whoever can prove or disprove the Hodge conjecture using "some argument". It was formulated by the Scottish mathematician William Vallance Douglas Hodge as a result of a work in between 1930 and 1940 to enrich the description of De Rham cohomology to include extra structure which is present in the case of complex algebraic varieties. Данное издание представляет собой компиляцию сведений, находящихся в свободном доступе в среде Интернет в целом, и в информационном...