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- Jacobian_conjecture abstract "In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrich Keller. It was widely publicized by Shreeram Abhyankar, as an example of a question in the area of algebraic geometry that requires little beyond a knowledge of calculus to state.What is perhaps the simplest unsolved case of the conjecture conveys its difficulty: Let f: ℂ2 → ℂ2 be a polynomial mapping. (That is, f(z,w) is of the form (P(z,w), Q(z,w)) where P and Q are polynomial mappings with complex coefficients). Assume further that f is locally one-to-one. Then the Jacobian conjecture asserts that the function f is both a) globally one-to-one and b) onto. (In other words, that f is a bijection of ℂ2 to itself.) Neither a) nor b) has been proved.The Jacobian conjecture is notorious for the large number of attempted proofs that turned out to contain subtle errors. As of 2015, there are no plausible claims to have proved it. Even the two variable case has resisted all efforts. There are no known compelling reasons for believing it to be true, and according to van den Essen (1997) there are some suspicions that the conjecture is in fact false for large numbers of variables.".
- Jacobian_conjecture wikiPageExternalLink purl?GDZPPN002200376.
- Jacobian_conjecture wikiPageExternalLink BF01695502.
- Jacobian_conjecture wikiPageExternalLink smf_sem-cong_2_55-81.pdf.
- Jacobian_conjecture wikiPageExternalLink jacobian.html.
- Jacobian_conjecture wikiPageID "1193823".
- Jacobian_conjecture wikiPageLength "11309".
- Jacobian_conjecture wikiPageOutDegree "23".
- Jacobian_conjecture wikiPageRevisionID "683665856".
- Jacobian_conjecture wikiPageWikiLink Algebraic_geometry.
- Jacobian_conjecture wikiPageWikiLink Calculus.
- Jacobian_conjecture wikiPageWikiLink Category:Algebraic_geometry.
- Jacobian_conjecture wikiPageWikiLink Category:Conjectures.
- Jacobian_conjecture wikiPageWikiLink Category:Polynomials.
- Jacobian_conjecture wikiPageWikiLink Coefficient.
- Jacobian_conjecture wikiPageWikiLink Crelles_Journal.
- Jacobian_conjecture wikiPageWikiLink Degree_of_a_polynomial.
- Jacobian_conjecture wikiPageWikiLink Determinant.
- Jacobian_conjecture wikiPageWikiLink Dixmier_conjecture.
- Jacobian_conjecture wikiPageWikiLink Function_(mathematics).
- Jacobian_conjecture wikiPageWikiLink Inverse_function_theorem.
- Jacobian_conjecture wikiPageWikiLink Jacobian_matrix.
- Jacobian_conjecture wikiPageWikiLink Jacobian_matrix_and_determinant.
- Jacobian_conjecture wikiPageWikiLink Journal_für_die_reine_und_angewandte_Mathematik.
- Jacobian_conjecture wikiPageWikiLink Mathematics.
- Jacobian_conjecture wikiPageWikiLink Maxim_Kontsevich.
- Jacobian_conjecture wikiPageWikiLink Morphism_of_algebraic_varieties.
- Jacobian_conjecture wikiPageWikiLink Multivariable_calculus.
- Jacobian_conjecture wikiPageWikiLink Ott-Heinrich_Keller.
- Jacobian_conjecture wikiPageWikiLink Partial_derivative.
- Jacobian_conjecture wikiPageWikiLink Polynomial.
- Jacobian_conjecture wikiPageWikiLink Regular_map_(algebraic_geometry).
- Jacobian_conjecture wikiPageWikiLink Shreeram_Abhyankar.
- Jacobian_conjecture wikiPageWikiLink Shreeram_Shankar_Abhyankar.
- Jacobian_conjecture wikiPageWikiLink Variable_(mathematics).
- Jacobian_conjecture wikiPageWikiLinkText "Formulation of the Jacobian conjecture".
- Jacobian_conjecture wikiPageWikiLinkText "Jacobian conjecture".
- Jacobian_conjecture first "A.".
- Jacobian_conjecture first "Alexei".
- Jacobian_conjecture first "Maxim".
- Jacobian_conjecture first "P.K.".
- Jacobian_conjecture hasPhotoCollection Jacobian_conjecture.
- Jacobian_conjecture id "J/j120010".
- Jacobian_conjecture last Maxim_Kontsevich.
- Jacobian_conjecture last "Adjamagbo".
- Jacobian_conjecture last "Belov-Kanel".
- Jacobian_conjecture last "van den Essen".
- Jacobian_conjecture title "Jacobian conjecture".
- Jacobian_conjecture wikiPageUsesTemplate Template:=.
- Jacobian_conjecture wikiPageUsesTemplate Template:Citation.
- Jacobian_conjecture wikiPageUsesTemplate Template:Eom.
- Jacobian_conjecture wikiPageUsesTemplate Template:Harvs.
- Jacobian_conjecture wikiPageUsesTemplate Template:Harvtxt.
- Jacobian_conjecture year "2007".
- Jacobian_conjecture subject Category:Algebraic_geometry.
- Jacobian_conjecture subject Category:Conjectures.
- Jacobian_conjecture subject Category:Polynomials.
- Jacobian_conjecture hypernym Problem.
- Jacobian_conjecture type Article.
- Jacobian_conjecture type Disease.
- Jacobian_conjecture type Type.
- Jacobian_conjecture type Article.
- Jacobian_conjecture type Conjecture.
- Jacobian_conjecture type Function.
- Jacobian_conjecture type Polynomial.
- Jacobian_conjecture type Statement.
- Jacobian_conjecture type Type.
- Jacobian_conjecture type Statement.
- Jacobian_conjecture comment "In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrich Keller. It was widely publicized by Shreeram Abhyankar, as an example of a question in the area of algebraic geometry that requires little beyond a knowledge of calculus to state.What is perhaps the simplest unsolved case of the conjecture conveys its difficulty: Let f: ℂ2 → ℂ2 be a polynomial mapping.".
- Jacobian_conjecture label "Jacobian conjecture".
- Jacobian_conjecture sameAs Conjecture_jacobienne.
- Jacobian_conjecture sameAs Jacobiaans_vermoeden.
- Jacobian_conjecture sameAs Congetura_jacobian-a.
- Jacobian_conjecture sameAs m.04g6f9.
- Jacobian_conjecture sameAs Проблема_якобиана.
- Jacobian_conjecture sameAs Q2605695.
- Jacobian_conjecture sameAs Q2605695.
- Jacobian_conjecture sameAs 雅可比猜想.
- Jacobian_conjecture wasDerivedFrom Jacobian_conjecture?oldid=683665856.
- Jacobian_conjecture isPrimaryTopicOf Jacobian_conjecture.