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Finiteness theorems for abelian varieties over number fields. (English) Zbl 0602.14044
Arithmetic geometry, Pap. Conf., Storrs/Conn. 1984, 9-27 (1986).
This is just the English translation of the author’s famous paper [Invent. Math. 73, 349-366 (1983; Zbl 0588.14026)] in which he proved the conjectures of Tate, Shafarevich and Mordell for number fields.
[For the entire collection see Zbl 0596.00007.]
Reviewer: L.Bădescu

MSC:
14K15 Arithmetic ground fields for abelian varieties
14G05 Rational points
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14G25 Global ground fields in algebraic geometry
11G50 Heights
11G10 Abelian varieties of dimension \(> 1\)
11D41 Higher degree equations; Fermat’s equation