van der Geer, Gerard (ed.) et al., Number fields and function fields – two parallel worlds. Boston, MA: Birkhäuser (ISBN 0-8176-4397-4/hbk; 0-8176-4447-4/e-book). Prog. Math. 239, 311-318 (2005).
Summary: R. Pink
and the author [in: Proc. ICM 2002, Beijing, China, Vol. I, 539–546 (2002; Zbl 1026.14012
)] gave a short proof of the Manin-Mumford conjecture, which was inspired by an earlier model-theoretic proof by Hrushovski. The proof given in [loc. cit.] uses a difficult unpublished ramification-theoretic result of Serre. It is the purpose of this note to show how the proof given in [loc. cit.] can be modified so as to circumvent the reference to Serre’s result. J. Oesterle and R. Pink contributed several simplifications and shortcuts to this note.
|14K05||Algebraic theory of abelian varieties|
|14K15||Arithmetic ground fields (abelian varieties)|