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Statements

Subject Item: dbr:Uniform_boundedness_conjecture_for_rational_points
rdfs:label: Uniform boundedness conjecture for rational points
rdfs:comment: In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field and a positive integer that there exists a number depending only on and such that for any algebraic curve defined over having genus equal to has at most -rational points. This is a refinement of Faltings's theorem, which asserts that the set of -rational points is necessarily finite.
dcterms:subject: dbc:Arithmetic_geometry dbc:Conjectures
dbo:wikiPageID: 66851658
dbo:wikiPageRevisionID: 1068255201
dbo:wikiPageWikiLink: dbr:Barry_Mazur dbr:David_Zureick-Brown dbr:Algebraic_curve dbr:Annals_of_Mathematics dbr:Bogomolov_conjecture dbc:Arithmetic_geometry dbr:Vessilin_Dimtrov dbr:Geometric_genus dbr:Chabauty's_method dbr:Arithmetic_geometry dbr:Mordell–Weil_theorem dbr:Eric_Katz dbr:Philipp_Habegger dbr:Ziyang_Gao dbr:Joe_Harris_(mathematician) dbr:Faltings's_theorem dbr:Bombieri–Lang_conjecture dbr:Number_field dbr:Lucia_Caporaso dbr:Rational_point dbc:Conjectures dbr:Jacobian_variety dbr:Joseph_Rabinoff dbr:Hyperelliptic_curve
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dbo:abstract: In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field and a positive integer that there exists a number depending only on and such that for any algebraic curve defined over having genus equal to has at most -rational points. This is a refinement of Faltings's theorem, which asserts that the set of -rational points is necessarily finite.
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Subject Item: dbr:Glossary_of_arithmetic_and_diophantine_geometry
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:Torsion_conjecture
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:Bombieri–Lang_conjecture
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:Uniform_boundedness_conjecture
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points
dbo:wikiPageDisambiguates: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:List_of_unsolved_problems_in_mathematics
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:Thue_equation
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:Mazur's_Conjecture_B
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points
dbo:wikiPageRedirects: dbr:Uniform_boundedness_conjecture_for_rational_points

Subject Item: dbr:Uniform_boundedness_conjecture_(rational_points)
dbo:wikiPageWikiLink: dbr:Uniform_boundedness_conjecture_for_rational_points
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