About: Uniform boundedness conjecture for rational points

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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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  • 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. (en)
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  • 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. (en)
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  • Uniform boundedness conjecture for rational points (en)
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