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Abstract  In this paper we complete our ‘second‐generation’ model‐theoretic account of the function field Mordell–Lang conjecture, where we avoid appeals to dichotomy theorems for (generalized) Zariski geometries. In the current paper we reduce the semiabelian case to the abelian case using model‐theoretic tools. We also use our results from Benoist, Bouscaren and Pillay [ J. Math. Log . 16 (2016)] to prove modularity of the ‘Manin kernels’ (overF  p(  t  )    s  e  pin positive characteristic and overC  (  t  )    a  l  gin characteristic 0).

On function field Mordell–Lang: the semiabelian case and the socle theorem