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Irreducible Subvarieties and Rational Points

American Journal of Mathematics, 1965
fields." In this paper we prove this conjecture by elementary considerations of algebraic geometry. Given an algebraic set V defined over a field k (always assumed to be perfect), we consider the set of all subvarieties (absolutely irreducible) of V which are defined over k.
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Rational points of the curve over

2014
Let q be a power of an odd prime. For arbitrary positive integers h, n, m with n dividing m and arbitrary with ? ? 0 we determine the number of -rational points of the curve in many cases.
Özbudak, Ferruh, Saygı, Zülfükar
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The Group of Rational Points

1992
In this chapter we will prove Mordell’s theorem that the group of rational points on a non-singular cubic is finitely generated. There is a tool used in the proof called the height. In brief, the height of a rational point measures how complicated the point is from the viewpoint of number theory.
Joseph H. Silverman, John T. Tate
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POINT RATIONING

Bulletin of the Oxford University Institute of Economics & Statistics, 1941
F. BURCHARDT., G. D. N. WORSWICK.
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