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- Manin_conjecture abstract "In mathematics, the Manin conjecture was proposed by Yuri I. Manin and his collaboratorsin 1989when theyinitiated a programwith the aim of describing the distribution of rational points on suitable algebraic varieties.Their main conjecture is as follows.Let be a Fano variety definedover a number field ,let be a height function which is relative to the anticanonical divisorand assume that is Zariski dense in . Then there existsa non-empty Zariski open subset such that the counting functionof -rational points of bounded height, defined byfor , satisfiesas Hereis the rank of the Picard group of and is a positive constant whichlater received a conjectural interpretation by Peyre.Manin's conjecture has been decided for certain families of varieties, but is still open in general.".
- Manin_conjecture thumbnail Rational_points_of_bounded_height_outside_the_27_lines_on_Clebsch's_diagonal_cubic_surface.png?width=300.
- Manin_conjecture wikiPageID "41912043".
- Manin_conjecture wikiPageRevisionID "601557232".
- Manin_conjecture subject Category:Conjectures.
- Manin_conjecture subject Category:Diophantine_geometry.
- Manin_conjecture subject Category:Number_Theory.
- Manin_conjecture comment "In mathematics, the Manin conjecture was proposed by Yuri I. Manin and his collaboratorsin 1989when theyinitiated a programwith the aim of describing the distribution of rational points on suitable algebraic varieties.Their main conjecture is as follows.Let be a Fano variety definedover a number field ,let be a height function which is relative to the anticanonical divisorand assume that is Zariski dense in .".
- Manin_conjecture label "Manin conjecture".
- Manin_conjecture sameAs m.0_qjp8h.
- Manin_conjecture sameAs Q17080204.
- Manin_conjecture sameAs Q17080204.
- Manin_conjecture wasDerivedFrom Manin_conjecture?oldid=601557232.
- Manin_conjecture depiction Rational_points_of_bounded_height_outside_the_27_lines_on_Clebsch's_diagonal_cubic_surface.png.
- Manin_conjecture isPrimaryTopicOf Manin_conjecture.