Siegel’s Theorem and Integral Points
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If C is an affine curve defined over a ring R finitely generated over Z, and if its genus is ≧ 1, then C has only a finite number of points in R. This is the central result of the chapter. We shall also give a relative formulation of it for a curve defined over a ring which is a finitely generated algebra over an arbitrary field k of characteristic 0. In that case, the presence of infinitely many points in R implies that the curve actually comes from a curve defined over the constant field and that its points are of a special nature (excluding possibly a finite number).
KeywordsIntegral Point Galois Group Abelian Variety Number Field Finite Type
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