Hodge conjecture
Hodge conjecture Millennium Prize Problems P versus NP The Hodge conjecture The Poincaré conjecture The Riemann hypothesis Yang-Mills existence ...
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Talk:Hodge conjecture
Talk:Hodge conjecture Unsolved problems in mathematics Please, can someone write a brief description of the conjecture? These two or three phrases (written as ... that must be tagged. Thanks! --surueña The conjecture states that for a smooth projective complex algebraic variety, every Hodge cycle in a space H p, ...
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Conjecture of Hodge   (translated from Italian)
Conjecture of Hodge conjecture of Hodge it is an important unsolved problem of ... equations that define the under-varieties. The conjecture is born from turns out you ...
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Poincaré conjecture
Poincaré conjecture Millennium Prize Problems P versus NP The Hodge conjecture The Poincaré conjecture The Riemann hypothesis Yang-Mills existence and ... and smoothness The Birch and Swinnerton-Dyer conjecture In mathematics, the Poincaré conjecture (see ...
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Hodge cycle
Hodge cycle In mathematics, a Hodge cycle is a particular kind of homology ... algebraic variety or Kähler manifold is a Hodge cycle, provided it satisfies two conditions. Firstly ... decomposition of H shown to exist in Hodge theory, x is purely of type (p ... the universal coefficient theorem). The conventional term Hodge cycle therefore is slightly inaccurate, in ...
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Tate conjecture
Tate conjecture In mathematics, the Tate conjecture is a 1963 conjecture of John Tate linking algebraic geometry, and ... case, as of 2005, and, like the Hodge conjecture to which it is related at ...
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Hodge theory
Hodge theory In mathematics, Hodge theory is one aspect of the study ... It was developed by W. V. D. Hodge in the 1930s as an extension of ... de Rham cohomology The original formulation of Hodge theory, due to W. V. D. Hodge, was for the de Rham complex. ...
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Talk:Hodge theory
Talk:Hodge theory This seems to be a definition of Hodge structure, which is what the self-proclaiimed "Hodge theorists" talk about -- namely those working on the Hodge conjecture. But from my point of view, ...
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Hodge index theorem
Hodge index theorem In mathematics, the Hodge index theorem for an algebraic surface V ... in the 1930s by W. V. D. Hodge, for varieties over the complex numbers, after it had been a conjecture for some time of the Italian school ... in this case showed that ρ < ∞). Hodge's methods were the topological ones ...
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W. V. D. Hodge
W. V. D. Hodge This article is about a mathematician. For the companion of Samuel Johnson, see Hodge (cat). William Vallance Douglas Hodge (17 June 1903 - 7 July 1975) was ... algebraic geometry and differential geometry - now called Hodge theory and pertaining more generally to Kähler ... of the Royal Society in 1974. The Hodge index theorem was a result on ...
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