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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.

##### MSC:
 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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