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

Vojta, Paul

Ann. Math. (2) 133, No. 3, 509-548 (1991).

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.

Reviewer: Koji Katayama (Tokyo)

MSC:

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

Keywords:

Mordell-Faltings theorem; rational points; Mordell’s conjecture; function field; Thue-Siegel-Dyson-Gel’fond theorem