Siegel’s theorem in the compact case. (English) Zbl 0774.14019

This is a very nice and interesting paper. Here the author gives a proof (not effectively computable for the upper bound of heights) of Mordell’s conjecture [Now Faltings’ theorem: Let \(C\) be a curve of genus \(>1\) defined over an algebraic number field \(k\). Then the set of all \(k\)-rational points of \(C\) is finite], different from Faltings’, being motivated by his own proof in the function field case and by the Thue-Siegel-Dyson-Gel’fond theorem.


14G05 Rational points
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
14H25 Arithmetic ground fields for curves
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