We consider abelian varieties, defined over essentially global fields, namely, those of §2, §3, §4, Chapter 2. We shall prove an absolute result and a relative one concerning the group of rational points of an abelian variety over such fields, namely:
Theorem 1. Let K be a finitely generated field over the prime field. Let A be an abelian variety defined over K. Then A(K) is finitely generated.
KeywordsAbelian Variety Number Field Finite Type Constant Field Abelian Extension
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
© Springer Science+Business Media New York 1983