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On function field Mordell–Lang and Manin–Mumford
2016
Journal of Mathematical Logic
We give a reduction of the function field Mordell-Lang conjecture to the function field Manin-Mumford conjecture, for abelian varieties, in all characteristics, via model theory, but avoiding recourse to the dichotomy theorems for (generalized) Zariski geometries. Additional ingredients include the "Theorem of the kernel", and a result of Wagner on commutative groups of finite Morley rank without proper infinite definable subgroups. In characteristic 0 the methods also yield another account of
doi:10.1142/s021906131650001x
fatcat:lhyxcmli55cv7kzlco4rji22zm