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Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell , [ 1 ] and known as the Mordell conjecture until its 1983 proof by Gerd Faltings . [ 2 ]
Upload file; Special pages ... Cite this page; Get shortened URL; Download QR code; Print/export Download as PDF; Printable version ... Rational curves are subdivided ...
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Rational Bézier curve – polynomial curve defined in homogeneous coordinates (blue) and its projection on plane – rational curve (red) In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, [1] [2] [3] are a system of coordinates used in projective geometry, just as Cartesian coordinates are used ...
The case with an elliptic curve and the field of rational numbers is Mordell's theorem, answering a question apparently posed by Henri Poincaré around 1901; it was proved by Louis Mordell in 1922. It is a foundational theorem of Diophantine geometry and the arithmetic of abelian varieties .
Mazur's conjecture B is a weaker variant of the uniform boundedness conjecture that asserts that there should be a number (,,) such that for any algebraic curve defined over having genus and whose Jacobian variety has Mordell–Weil rank over equal to , the number of -rational points of is at most (,,).
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